91Ó°ÊÓ

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. $$ \int_{1}^{\infty} \frac{1}{\sqrt{e^{x}-x}} d x $$

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

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. $$ \int_{1}^{\infty} \frac{1}{e^{x}-2^{x}} d x $$

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. $$ \int \frac{1}{1-\csc x} d x $$

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. $$ \int_{-\infty}^{\infty} \frac{d x}{\sqrt{x^{4}+1}} $$

Evaluate each integral in Exercises \(63-70\) by eliminating the square root. $$ \int_{0}^{2 \pi} \sqrt{\frac{1-\cos x}{2}} d x $$

Use reduction formulas to evaluate the integrals. \(\int 8 \cot ^{4} t d t\)

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. $$ \int_{-\infty}^{\infty} \frac{d x}{e^{x}+e^{-x}} $$

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

Evaluate each integral in Exercises \(63-70\) by eliminating the square root. $$ \int_{0}^{\pi} \sqrt{1-\cos 2 x} d x $$