"Use the indicated value of u to rewrite..." was answered by students like you

sklicatias

Answered question

2021-12-07

Use the indicated value of u to rewrite the given integral in terms of the variable u.

\int \frac{e^{4 x}}{{(1 + e^{2 x})}^{4}} d x, u = e^{2 x}

Fommeirj

Beginner2021-12-08Added 11 answers

Step 1
Given

\int \frac{e^{4 x}}{{(1 + e^{2 x})}^{4}} d x, u = e^{2 x}

Step 2

I = \int \frac{e^{4 x}}{{(1 + e^{2 x})}^{4}} d x

u = e^{2 x}

d u = 2 e^{2 x} d x = 2 u d x

e^{4 x} d x = \frac{u^{2}}{2 u} d u = \frac{u}{2} d u

I = \frac{1}{2} \int \frac{u}{{(1 + u)}^{4}} d u

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