Anti-derivative of $frac{exp(x)-1}{x}$Proving that $exp(z_1+z_2) = exp(z_1)exp(z_2)$ with power...
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Anti-derivative of $frac{exp(x)-1}{x}$
Proving that $exp(z_1+z_2) = exp(z_1)exp(z_2)$ with power seriesIntegrate $int_{-infty}^{infty}expleft(-frac{pi^2t(2x+1)^2}{2c^2}right)cosleft(frac{(2x+1)pi y}{c}right)exp(-2pi i kx)dx$Integral of exp(a/x)How to find the area for the curve $y=sin^3(2x)cos^3(2x)$?Why does $zmapsto exp(-z^2)$ have an antiderivative on $mathbb C$?Trouble with indefinite integral $ int sqrt{csc x-sin x} dx $computation of $int_{0}^{infty}frac{1}{theta^{2n+1}}expleft(- frac1{theta^2}sum_{i=1}^n x_i^2right)dtheta$How to find $b_n$ for the limit comparison test in $sum_{n=1}^{infty}frac{(ln(n))^2}{sqrt{n}(10n-9sqrt{n})}$.I need help calculating the anti derivative of $f(x)=2* frac{c^{2x+1}}{2x+1}$Computing $I'(x)$ of $I(x)=int_{-exp(x)}^{x^2}cos(xt^2) dt$
$begingroup$
I am looking for the antiderivative of $$frac{exp(x)-1}{x}$$ I showed that it is equivalent to calculate $$sum_{n=1}^{infty}frac1n frac{x^n}{n!}$$ but I can't find both of the solutions. If someone could help me I would very appreciate it. Thanks!
calculus integration power-series indefinite-integrals
asked Mar 10 at 14:56
OdysOdys
11
$endgroup$
add a comment |
$begingroup$
I am looking for the antiderivative of $$frac{exp(x)-1}{x}$$ I showed that it is equivalent to calculate $$sum_{n=1}^{infty}frac1n frac{x^n}{n!}$$ but I can't find both of the solutions. If someone could help me I would very appreciate it. Thanks!
calculus integration power-series indefinite-integrals
asked Mar 10 at 14:56
OdysOdys
11
$endgroup$
3
$begingroup$
For $xne0$, this is equivalent to compute the antiderivative of $e^x/x$, which cannot be expressed in terms of elementary functions.
$endgroup$
– egreg
Mar 10 at 15:01
4
$begingroup$
You can write the solution in terms of this non-elementary function.
$endgroup$
– J.G.
Mar 10 at 15:03
add a comment |
$begingroup$
I am looking for the antiderivative of $$frac{exp(x)-1}{x}$$ I showed that it is equivalent to calculate $$sum_{n=1}^{infty}frac1n frac{x^n}{n!}$$ but I can't find both of the solutions. If someone could help me I would very appreciate it. Thanks!
calculus integration power-series indefinite-integrals
asked Mar 10 at 14:56
OdysOdys
11
$endgroup$
I am looking for the antiderivative of $$frac{exp(x)-1}{x}$$ I showed that it is equivalent to calculate $$sum_{n=1}^{infty}frac1n frac{x^n}{n!}$$ but I can't find both of the solutions. If someone could help me I would very appreciate it. Thanks!
calculus integration power-series indefinite-integrals
calculus integration power-series indefinite-integrals
asked Mar 10 at 14:56
OdysOdys
11
asked Mar 10 at 14:56
OdysOdys
11
edited Mar 10 at 15:43
Odys
asked Mar 10 at 14:56
OdysOdys
11
asked Mar 10 at 14:56
OdysOdys
11
asked Mar 10 at 14:56
OdysOdys
11
11
3
$begingroup$
For $xne0$, this is equivalent to compute the antiderivative of $e^x/x$, which cannot be expressed in terms of elementary functions.
$endgroup$
– egreg
Mar 10 at 15:01
4
$begingroup$
You can write the solution in terms of this non-elementary function.
$endgroup$
– J.G.
Mar 10 at 15:03
add a comment |
3
$begingroup$
For $xne0$, this is equivalent to compute the antiderivative of $e^x/x$, which cannot be expressed in terms of elementary functions.
$endgroup$
– egreg
Mar 10 at 15:01
4
$begingroup$
You can write the solution in terms of this non-elementary function.
$endgroup$
– J.G.
Mar 10 at 15:03
3
3
$begingroup$
For $xne0$, this is equivalent to compute the antiderivative of $e^x/x$, which cannot be expressed in terms of elementary functions.
$endgroup$
– egreg
Mar 10 at 15:01
$begingroup$
For $xne0$, this is equivalent to compute the antiderivative of $e^x/x$, which cannot be expressed in terms of elementary functions.
$endgroup$
– egreg
Mar 10 at 15:01
4
4
$begingroup$
You can write the solution in terms of this non-elementary function.
$endgroup$
– J.G.
Mar 10 at 15:03
$begingroup$
You can write the solution in terms of this non-elementary function.
$endgroup$
– J.G.
Mar 10 at 15:03
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
As long as you cannot use the exponential integral function, leave it as you wrote
$$intfrac{e^x-1}{x},dx=sum_{n=1}^{infty}frac1n frac{x^n}{n!}>sum_{n=1}^{infty}frac1{n+1} frac{x^n}{n!}=frac 1xsum_{n=1}^{infty} frac{x^{n+1}}{(n+1)!}=frac{e^x-x-1}x$$
answered Mar 10 at 15:57
Claude LeiboviciClaude Leibovici
124k1157135
$endgroup$
$begingroup$
ok, thank you for your answer !
$endgroup$
– Odys
Mar 11 at 16:33
$begingroup$
@Odys. You are welcome ! You did a good job. Sooner or later, you will learn a lot about special functions and ... you will enjoy them. Cheers :-)
$endgroup$
– Claude Leibovici
Mar 11 at 17:22
add a comment |
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$begingroup$
As long as you cannot use the exponential integral function, leave it as you wrote
$$intfrac{e^x-1}{x},dx=sum_{n=1}^{infty}frac1n frac{x^n}{n!}>sum_{n=1}^{infty}frac1{n+1} frac{x^n}{n!}=frac 1xsum_{n=1}^{infty} frac{x^{n+1}}{(n+1)!}=frac{e^x-x-1}x$$
answered Mar 10 at 15:57
Claude LeiboviciClaude Leibovici
124k1157135
$endgroup$
$begingroup$
ok, thank you for your answer !
$endgroup$
– Odys
Mar 11 at 16:33
$begingroup$
@Odys. You are welcome ! You did a good job. Sooner or later, you will learn a lot about special functions and ... you will enjoy them. Cheers :-)
$endgroup$
– Claude Leibovici
Mar 11 at 17:22
add a comment |
$begingroup$
As long as you cannot use the exponential integral function, leave it as you wrote
$$intfrac{e^x-1}{x},dx=sum_{n=1}^{infty}frac1n frac{x^n}{n!}>sum_{n=1}^{infty}frac1{n+1} frac{x^n}{n!}=frac 1xsum_{n=1}^{infty} frac{x^{n+1}}{(n+1)!}=frac{e^x-x-1}x$$
answered Mar 10 at 15:57
Claude LeiboviciClaude Leibovici
124k1157135
$endgroup$
$begingroup$
ok, thank you for your answer !
$endgroup$
– Odys
Mar 11 at 16:33
$begingroup$
@Odys. You are welcome ! You did a good job. Sooner or later, you will learn a lot about special functions and ... you will enjoy them. Cheers :-)
$endgroup$
– Claude Leibovici
Mar 11 at 17:22
add a comment |
$begingroup$
As long as you cannot use the exponential integral function, leave it as you wrote
$$intfrac{e^x-1}{x},dx=sum_{n=1}^{infty}frac1n frac{x^n}{n!}>sum_{n=1}^{infty}frac1{n+1} frac{x^n}{n!}=frac 1xsum_{n=1}^{infty} frac{x^{n+1}}{(n+1)!}=frac{e^x-x-1}x$$
answered Mar 10 at 15:57
Claude LeiboviciClaude Leibovici
124k1157135
$endgroup$
As long as you cannot use the exponential integral function, leave it as you wrote
$$intfrac{e^x-1}{x},dx=sum_{n=1}^{infty}frac1n frac{x^n}{n!}>sum_{n=1}^{infty}frac1{n+1} frac{x^n}{n!}=frac 1xsum_{n=1}^{infty} frac{x^{n+1}}{(n+1)!}=frac{e^x-x-1}x$$
answered Mar 10 at 15:57
Claude LeiboviciClaude Leibovici
124k1157135
answered Mar 10 at 15:57
Claude LeiboviciClaude Leibovici
124k1157135
answered Mar 10 at 15:57
Claude LeiboviciClaude Leibovici
124k1157135
answered Mar 10 at 15:57
Claude LeiboviciClaude Leibovici
124k1157135
124k1157135
$begingroup$
ok, thank you for your answer !
$endgroup$
– Odys
Mar 11 at 16:33
$begingroup$
@Odys. You are welcome ! You did a good job. Sooner or later, you will learn a lot about special functions and ... you will enjoy them. Cheers :-)
$endgroup$
– Claude Leibovici
Mar 11 at 17:22
add a comment |
$begingroup$
ok, thank you for your answer !
$endgroup$
– Odys
Mar 11 at 16:33
$begingroup$
@Odys. You are welcome ! You did a good job. Sooner or later, you will learn a lot about special functions and ... you will enjoy them. Cheers :-)
$endgroup$
– Claude Leibovici
Mar 11 at 17:22
$begingroup$
ok, thank you for your answer !
$endgroup$
– Odys
Mar 11 at 16:33
$begingroup$
ok, thank you for your answer !
$endgroup$
– Odys
Mar 11 at 16:33
$begingroup$
@Odys. You are welcome ! You did a good job. Sooner or later, you will learn a lot about special functions and ... you will enjoy them. Cheers :-)
$endgroup$
– Claude Leibovici
Mar 11 at 17:22
$begingroup$
@Odys. You are welcome ! You did a good job. Sooner or later, you will learn a lot about special functions and ... you will enjoy them. Cheers :-)
$endgroup$
– Claude Leibovici
Mar 11 at 17:22
add a comment |
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$begingroup$
For $xne0$, this is equivalent to compute the antiderivative of $e^x/x$, which cannot be expressed in terms of elementary functions.
$endgroup$
– egreg
Mar 10 at 15:01
4
$begingroup$
You can write the solution in terms of this non-elementary function.
$endgroup$
– J.G.
Mar 10 at 15:03