How do you integrate $\int e^{x} sec x d x$ $int e^x sec x dx$ using integration by parts?

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How do you integrate $\int e^{x} sec x d x$ $int e^x sec x dx$ using integration by parts?

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Answer 1 · 2016-12-14T18:41:55

Let $u = sec x$ $u = secx$ and $d v = e^{x} d x$ $dv = e^x dx$

Explanation:

Then

$\int e^{x} sec x d x = e^{x} sec x - \int e^{x} sec x tan x d x$ $int e^x secx dx = e^x sec x -int e^x secx tanx dx$

Which WolframAlpha gives as:

$= e^{x} sec x - (1 - i) e^{(1 + i) x} l_{2} F_{1} (\frac{1}{2} - \frac{i}{2}, 1; \frac{3}{2} - \frac{i}{2}; - e^{2 i x})$ $= e^x secx -(1-i)e^((1+i)x) color(white)(l)_2F_1(1/2-i/2,1;3/2-i/2;-e^(2ix))$

Where $l_{2} F_{1} (a, b; c; x)$ $color(white)(l)_2F_1(a,b;c;x)$ is the hypergeometric function.

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How do you integrate $\int e^{x} sec x d x$ $int e^x sec x dx$ using integration by parts?

1 Answer

Explanation:

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