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JH

# Evaluate the integral.$\displaystyle \int_0^1 \frac{1 + 12t}{1 + 3t}\ dt$

## $4-\ln 4$

#### Topics

Integration Techniques

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##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

because we have polynomial divided by polynomial and they're both too The first power I would go ahead and do long division here, so go using the polynomial division to simplify the inside weaken right. This is for that's the kosher. Remainder is negative three and then we have one plus bt on the bottom. So So this is from using just doing the polynomial division and then you can see our new integral is easier than the original. So the internal afore we know that she's fourteen here. If this three in front of the T and this plus one is bothering you, you can go ahead and use the use up here, from which you can see that do you equals three dt So I won't write out the full details there. But if this may help you integrate, then we have minus three natural log one plus three tea and then we'LL also have to divide by three due to this in the use of our end point zero one and then cross off those threes. So plug in the one first for tea, we just get a four and then plug it into the natural line your natural log before. And then when you plug in zero for tea both. Herms Laura zero. So that's your final answer.

JH

#### Topics

Integration Techniques

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp