@Aditya Parson
–
Pls tell me how to solve this integral with the Ei(x) function..
–
Krishna Jha
·
4 years, 1 month 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?)
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Piyal De
·
4 years, 1 month ago

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@Piyal De
–
Man... You missed out a z....the integral is
\(\int\mathrm{e}^{tanz}z(sec^{2}z)\mathrm{d}z\).... coz there was an \(arctan(x)\) there... u have to back substitute \(arctan(x)=z\)... Now please solve this further... :-P..
–
Krishna Jha
·
4 years, 1 month ago

## Comments

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TopNewestHere \(tan^{-1}x\) is the inverse tangent function and can also be written as \(arctan(x)\). – Krishna Jha · 4 years, 1 month ago

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Why not use integration by parts – Tanmay Bhoite · 4 years, 1 month ago

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– Krishna Jha · 4 years, 1 month ago

Use it and show me how do u do it...Log in to reply

\[\frac{1}{2} e^i i \text{Ei}(-i+x)-\frac{1}{2} i e^{-i} \text{Ei}(i+x)+e^x \tan ^{-1}(x)\] – Louie Tan Yi Jie · 4 years, 1 month ago

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– Krishna Jha · 4 years, 1 month ago

HOW???Log in to reply

– Jimmi Simpson · 4 years, 1 month ago

Wolfram | AlphaLog in to reply

You should check this. – Aditya Parson · 4 years, 1 month ago

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– Krishna Jha · 4 years, 1 month ago

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

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 · 4 years, 1 month ago

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– Krishna Jha · 4 years, 1 month ago

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

– Piyal De · 4 years, 1 month ago

My bad!!!...Sorry sorry...Log in to reply