(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the definite integrals.

2. Relevant equations

Integral of (t+1)/(t^2+2t+1) dt from 1 to 4 (a=1, b=4)

and

Integral of (xe^(x^2+1)) dx from 0 to 2 (a=0, b=2)

3. The attempt at a solution

I have done them out, just wondering if this is the best way to do them, and perhaps if I made a mistake, it would be nice to know why:

For the first one, I factored and got:

(t+1) / ((t+1)(t+1))

then i cancelled and got

1 / (t+1)

Which then means:

ln |t+1| from 1 to 4 = ln |5| - ln |2|

Is that the answer for that?

Now, for the second one, I did the same thing:

antiderivative of (xe^(x^2+1)) = 1/2 (e^(x^2+1)...

right? Then the answer would be from 0 to 2:

e^5 - e^1 = e^4

Any feedback would be great.

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# Homework Help: Definite Integrals

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