91影视

Evaluate the following integrals, which have irreducible quadratic factors. \(\int \frac{2}{(x-4)\left(x^{2}+2 x+6\right)} d x\)

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.) \(\int \sqrt{\sin x} \cos x d x\)

Use the technique of completing the square to evaluate the following integrals. $$ \int \frac{1}{\sqrt{x^{2}+4 x-12}} d x $$

Approximate \(\int_{2}^{4} \frac{1}{\ln x} d x\) using the trapezoidal rule with eight subdivisions to four decimal places.

Compute the definite integrals. Use a graphing utility to confirm your answers. $$ \int_{0}^{1} x e^{-2 x} d x \text { (Express the answer in exact form.) } $$

Use tables to evaluate the integrals. You may need to complete the square or change variables to put the integral into a form given in the table. $$ \int \frac{\cos x}{\sin ^{2} x+2 \sin x} d x $$

Evaluate the integrals. If the integral diverges, answer "diverges."\(\int_{0}^{1} \frac{d x}{x^{\pi}}\)

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.) \(\int \sqrt{\sin x} \cos ^{3} x d x\)

Use the trapezoidal rule with four subdivisions to estimate \(\int_{0}^{0.8} x^{3} d x\) to four decimal places.

Use tables to evaluate the integrals. You may need to complete the square or change variables to put the integral into a form given in the table. $$ \int \frac{\arctan \left(x^{3}\right)}{x^{4}} d x $$