Evaluate the following integrals. int_{ln2}^{ln3}frac{e^x+e^{-x}}{e^{2x}-2+e^{-2x}}dx

nagasenaz 2020-11-01 Answered
Evaluate the following integrals.
ln2ln3ex+exe2x2+e2xdx
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Expert Answer

Asma Vang
Answered 2020-11-02 Author has 93 answers
To evaluate:
ln2ln3ex+exe2x2+e2xdx
We have,
(exex)2=e2x2+e2x
Thus,
ln2ln3ex+exe2x2+e2xdx=ln2ln3ex+ex(exex)2dx
Substitute, exex=u(ex+ex)dx=du
Therefore, becomes
ln2ln3ex+exe2x2+e2xdx=32831(u)2du
3283u2du
=[u11]3283
=[1u]3283
=38+23
=9+1624
=724
ln2ln3ex+exe2x2+e2xdx=724
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