91影视

Use a calculator or CAS to evaluate the following integrals. $$ \int \frac{d x}{x^{2}+4 x+13} $$

Approximate the integral to three decimal places using the indicated rule. \(\int_{0}^{0.4} \sin \left(x^{2}\right) d x ;\) Simpson's rule; \(n=4\)

Use the method of partial fractions to evaluate each of the following integrals. \(\int \frac{2-x}{x^{2}+x} d x\)

Find the integral by using the simplest method. Not all problems require integration by parts. $$ \int x^{3} e^{x} d x $$

Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge.\(\int_{1}^{\infty} \frac{5}{x^{3}} d x\)

Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. (Note: Some of the problems may be done using techniques of integration learned previously.) \(\int \cos ^{3} x d x\)

Approximate the integral to three decimal places using the indicated rule. \(\int_{0.1}^{0.5} \frac{\cos x}{x} d x ;\) trapezoidal rule; \(n=4\)

Use a calculator or CAS to evaluate the following integrals. $$ \int \frac{d x}{1+\sin x} $$

Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge.\(\int_{3}^{5} \frac{5}{(x-4)^{2}} d x\)

Use the method of partial fractions to evaluate each of the following integrals. \(\int \frac{2}{x^{2}-x-6} d x\)