How do you find $\int x \cdot sec x d x$ $int x*secxdx$ ?

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How do you find $\int x \cdot sec x d x$ $int x*secxdx$ ?

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Answer 1 · 2016-11-29T13:31:10

That cannot be evaluated by introductory level functions.

Explanation:

The integral involves the Polylogarithm function $L i_{2} (x) = \infty \sum k = 1 \frac{x^{k}}{k^{2}}$ $Li_2(x) = sum_(k=1)^oo x^k/k^2$ .

WolframAlpha gives

$\int x sec x d x = i (L i_{2} (- i e^{i x}) - L i_{2} (i e^{i x})) + x (ln (1 - i e^{i x}) - ln (1 + i e^{i x})) + C$ $int x secx dx = i(Li_2(-ie^(ix))-Li_2(ie^(ix)))+x(ln(1-ie^(ix))-ln(1+ie^(ix))) +C$

You can read more about the polylogarithm here: http://mathworld.wolfram.com/Polylogarithm.html

and here: https://en.wikipedia.org/wiki/Polylogarithm

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How do you find $\int x \cdot sec x d x$ $int x*secxdx$ ?

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