91Ó°ÊÓ

You are given a pair of integrals. Evaluate the integral that can be worked using the techniques covered so far (the other cannot). $$\int \frac{5}{3+x^{2}} d x \quad \text { and } \quad \, \int \frac{5}{3+x^{3}} d x$$

Use a comparison to determine whether the integral converges or diverges. $$\int_{1}^{\infty} \frac{2+\sec ^{2} x}{x} d x$$

You are given a pair of integrals. Evaluate the integral that can be worked using the techniques covered so far (the other cannot). $$\int \sin 2 x \, d x \quad \text { and } \quad \, \int \sin ^{2} x d x$$

Use a comparison to determine whether the integral converges or diverges. $$\int_{0}^{\infty} \frac{3}{x+e^{x}} d x$$

Use a comparison to determine whether the integral converges or diverges. $$\int_{1}^{\infty} e^{-x^{3}} d x$$

Use a comparison to determine whether the integral converges or diverges. $$\int_{0}^{\infty} \frac{\sin ^{2} x}{1+e^{x}} d x$$

You are given a pair of integrals. Evaluate the integral that can be worked using the techniques covered so far (the other cannot). $$\int \sec x \, d x \quad \text { and } \, \int \sec ^{2} x d x$$

Evaluate the integral using the reduction formulas from exercises 39 and 40 and (2.4). $$\int_{0}^{\pi / 2} \sin ^{4} x d x$$

Use a comparison to determine whether the integral converges or diverges. $$\int_{2}^{\infty} \frac{\ln x}{e^{x}+1} d x$$

Use a comparison to determine whether the integral converges or diverges. $$\int_{2}^{\infty} \frac{x^{2} e^{x}}{\ln x} d x$$