Evaluate the integrals. The integrals are listed in random order so you need to

beljuA

beljuA

Answered question

2021-10-17

Evaluate the integrals. The integrals are listed in random order so you need to decide which integration technique to use.
(exex)(ex+ex)3dx

Answer & Explanation

Vasquez

Vasquez

Expert2021-11-16Added 669 answers

Let u2=ex+ex. Then du2=(exex)dx, so 1exexdu2=dx. Rewrite using u2 and du2.

 

Let u2=ex+ex. Find du2dx

Differentiate ex+ex.

ddx[ex+ex]

 

By the Sum Rule, the derivative of ex+ex with respect to x is ddx[ex]+ddx[ex]

Differentiate using the Exponential Rule which states that ddx[ax] is axln(a) where a=e.

ex+ddx[ex]

Evaluate ddx[ex].

exex

Rewrite the problem using u2 and du2.

u23du2

By the Power Rule, the integral of u23 with respect to u2 is 14u24.

14u24+C

Replace all occurrences of u2 with ex+ex.

14(ex+ex)4+C

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