Morgan D.

# Indefinite/Definite Integrals

I need help solving a couple of indefinite/definite integrals. It seems all of my homework problems have done the less complicated ones so I'm not sure how to do these ones:

First problem: INDEFINITE
(integral symbol)((2x+3)/(x^2+3x-10)^3))dx

Second problem: DEFINITE
(integral symbol-WITH 0 AT BOTTOM AND 1 AT TOP)((e^(2x)/(1+sqrt of e^2x))dx

I'm very confused on how to do most of these so if there's a basic way to do it I'd love to learn it as I can't post every problem on here (although each one is more complicated than the last)

Thank you!

## 2 Answers By Expert Tutors

By: Tutor
New to Wyzant

A math tutor that is both knowledgeable and patient in secondary math. Bill P.

I did not notice the third power in the denominator (or is this exponent for the whole fraction?).

I will assume it is in the denominator. Then we have (1/u^3) du or u^-3 du.

the integration of that would be -1/2 (u^-2). Then substitute the u with x^2 + 3x -10 as before
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04/21/16 Tutor
4.8 (62)

Calculus will seem easy if you have the right tutor! Bill P.

I believe that one is u raised to the power of 3 in the denominator or 1/u^3.

I rewrote that as u raised to the power of negative 3 and took it from there.
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04/21/16

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