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JH

# Evaluate the integral.$\displaystyle \int_0^1 \frac{x}{(2x + 1)^3}\ dx$

## $\frac{1}{18}$

#### Topics

Integration Techniques

### Discussion

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##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

Let's use a U sub for the following. Take you to be two and two plus one. Then here this's equivalents who X equals you minus one over two. And we also have do you over too equals the X for us. Rewrite this one half. Now we have X so that we could use this over here. Then we have our do you We already took out the two over here. And then here we have you. Cute. What? And let's change those limits. If X equals zero, we'LL see you equals one. If that's equals one, then we see U equals three. So that's opera limit. So here, luscious rewrite this. And then we could go ahead and split this into two two fractions and then use the power rule. No plug in your end points. So here, planning the three first? No. Then plug in one. And this should end up simplifying too. One over eighteen. Wait. And that's our answer

JH

#### Topics

Integration Techniques

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp