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Activity 5.4.4 .
Evaluate each of the following indefinite integrals.
(a)
\(\displaystyle \int x^2 \sin(x) \, dx\)
(b)
\(\displaystyle \int t^3 \ln(t) \, dt\)
(c)
\(\displaystyle \int e^z \sin(z) \, dz\)
(d)
\(\displaystyle \int s^2 e^{3s} \, ds\)
(e)
\(\displaystyle \int t \arctan(t) \,dt\) (
Hint: At a certain point in this problem, it is very helpful to note that
\(\frac{t^2}{1+t^2} = 1 - \frac{1}{1+t^2}\text{.}\) )
