91Ó°ÊÓ

Use a CAS to evaluate the definite integrals. If the CAS does not give an exact answer in terms of elementary functions, then give a numerical approximation. $$ \int_{0}^{\pi / 2} \frac{1}{1+2 \cos ^{5} x} d x $$

Perform the indicated integrations. $$ \int \frac{e^{\tan ^{-1} 2 t}}{1+4 t^{2}} d t $$

Perform the indicated integrations. $$ \int(t+1) e^{-t^{2}-2 t-5} d t $$

Use the method of partial fraction decomposition to perform the required integration. \(\int_{4}^{6} \frac{x-17}{x^{2}+x-12} d x\)

Use a CAS to evaluate the definite integrals. If the CAS does not give an exact answer in terms of elementary functions, then give a numerical approximation. $$ \int_{-\pi / 4}^{\pi / 4} \frac{x^{3}}{4+\tan x} d x $$

apply integration by parts twice to evaluate each integral. $$ \int x^{5} e^{x^{2}} d x $$

apply integration by parts twice to evaluate each integral. $$ \int \ln ^{2} z d z $$

Perform the indicated integrations. $$ \int \frac{y}{\sqrt{16-9 y^{4}}} d y $$

Use a CAS to evaluate the definite integrals. If the CAS does not give an exact answer in terms of elementary functions, then give a numerical approximation. $$ \int_{2}^{3} \frac{x^{2}+2 x-1}{x^{2}-2 x+1} d x $$

Use the method of partial fraction decomposition to perform the required integration. \(\int_{0}^{\pi / 4} \frac{\cos \theta}{\left(1-\sin ^{2} \theta\right)\left(\sin ^{2} \theta+1\right)^{2}} d \theta\)