91Ó°ÊÓ

Use reduction formulas to evaluate the integrals. \(\int 9 \sin ^{3} \theta \cos ^{3 / 2} \theta d \theta\)

In Exercises \(35-64\) , use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integrals for convergence. If more than one method applies, use whatever method you prefer. $$ \int_{2}^{\infty} \frac{1}{\ln x} d x $$

Use numerical integration to estimate the value of $$ \pi=4 \int_{0}^{1} \frac{1}{1+x^{2}} d x $$

Use reduction formulas to evaluate the integrals. \(\int 2 \sin ^{2} t \sec ^{4} t d t\)

In Exercises \(35-64\) , use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integrals for convergence. If more than one method applies, use whatever method you prefer. $$ \int_{1}^{\infty} \frac{e^{x}}{x} d x $$

Evaluate each integral in Exercises \(57-62\) by multiplying by a form of 1 and using a substitution (if necessary) to reduce it to standard form. $$ \int \frac{1}{\sec \theta+\tan \theta} d \theta $$

Use reduction formulas to evaluate the integrals. \(\int \csc ^{2} y \cos ^{5} y d y\)

In Exercises \(35-64\) , use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integrals for convergence. If more than one method applies, use whatever method you prefer. $$ \int_{e}^{\infty} \ln (\ln x) d x $$

Evaluate each integral in Exercises \(57-62\) by multiplying by a form of 1 and using a substitution (if necessary) to reduce it to standard form. $$ \int \frac{1}{\csc \theta+\cot \theta} d \theta $$

Use reduction formulas to evaluate the integrals. \(\int 4 \tan ^{3} 2 x d x\)