Please solve this integral

extan1xdx\int \mathrm{e}^x tan^{-1}x\mathrm{d}x

Note by Krishna Jha
6 years, 3 months ago

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3 votes

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Here tan1xtan^{-1}x is the inverse tangent function and can also be written as arctan(x)arctan(x).

Krishna Jha - 6 years, 3 months ago

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Take z=arctan(x), then take dz =dx/(1+x^2)=dx/(1+tan^2z)=dx/(sec^2x)..................so dx=dz(sec^2z)...............so the integral reduces to [ integral e^(tan(z)) sec^2(z)) dz.....now substitute y=tan(z).....and tada u'll ger it!! Hope u understand it.........

(N.B..here sec^2(z) means sec squared z.................okay?)

Piyal De - 6 years, 3 months ago

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Man... You missed out a z....the integral is etanzz(sec2z)dz\int\mathrm{e}^{tanz}z(sec^{2}z)\mathrm{d}z.... coz there was an arctan(x)arctan(x) there... u have to back substitute arctan(x)=zarctan(x)=z... Now please solve this further... :-P..

Krishna Jha - 6 years, 3 months ago

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My bad!!!...Sorry sorry...

Piyal De - 6 years, 3 months ago

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You should check this.

Aditya Parson - 6 years, 3 months ago

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Pls tell me how to solve this integral with the Ei(x) function..

Krishna Jha - 6 years, 3 months ago

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12eiiEi(i+x)12ieiEi(i+x)+extan1(x)\frac{1}{2} e^i i \text{Ei}(-i+x)-\frac{1}{2} i e^{-i} \text{Ei}(i+x)+e^x \tan ^{-1}(x)

Louie Tan Yi Jie - 6 years, 3 months ago

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HOW???

Krishna Jha - 6 years, 3 months ago

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Wolfram | Alpha

Jimmi Simpson - 6 years, 3 months ago

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Why not use integration by parts

Tanmay Bhoite - 6 years, 3 months ago

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Use it and show me how do u do it...

Krishna Jha - 6 years, 3 months ago

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