Activity 5.4.2

Evaluate each of the following indefinite integrals. Check each antiderivative that you find by differentiating.

1. $\displaystyle \int te^{-t} \, dt$

2. $\displaystyle \int 4x \sin(3x) \, dx$

3. $\displaystyle \int z \sec^2(z) \,dz$

   Note: after applying integration by parts, we need to evaluate $\int \tan(z) \, dz$. To do so, recall that $\tan(z) = \frac{\sin(z)}{\cos(z)}$ and think about a $u$-substitution that leads to an antiderivative for $\tan(z)$.

4. $\displaystyle \int x \ln(x) \, dx$