Activity 5.4.4

Evaluate each of the following indefinite integrals.

1. $\displaystyle \int x^2 \sin(x) \, dx$

2. $\displaystyle \int t^3 \ln(t) \, dt$

3. $\displaystyle \int e^z \sin(z) \, dz$

4. $\displaystyle \int s^2 e^{3s} \, ds$

5. $\displaystyle \int t \arctan(t) \,dt$ (Hint: At a certain point in this problem, it is very helpful to note that $\frac{t^2}{1+t^2} = 1 - \frac{1}{1+t^2}$.)