Chapter 7

Evaluate the integral. $$\int \frac{\sqrt{x^{2}-9}}{x} d x$$

Write out the form of the partial fraction decomposition. (Do not find the numerical values of the coefficients.) $$\frac{4 x^{3}-x}{\left(x^{2}+5\right)^{2}}$$

Evaluate the integrals by making appropriate \(u\) -substitutions and applying the formulas reviewed in this section. $$\int e^{x} \sinh \left(e^{x}\right) d x$$

Evaluate the integrals that converge. $$\int_{2}^{+\infty} \frac{1}{x \sqrt{\ln x}} d x$$

Evaluate the integral. $$\int x^{2} \sin x d x$$

(a) Use the End paper Integral Table to evaluate the given integral. (b) If you have a CAS, use it to evaluate the integral, and then confirm that the result is equivalent to the one that you found in part (a). $$\int \frac{1}{x \sqrt{3 x-4}} d x$$

Evaluate the integral. $$\int \sin ^{3} x \cos ^{3} x d x$$

Evaluate the integral. $$\int \frac{d x}{x^{2} \sqrt{x^{2}-16}}$$

Write out the form of the partial fraction decomposition. (Do not find the numerical values of the coefficients.) $$\frac{1-3 x^{4}}{(x-2)\left(x^{2}+1\right)^{2}}$$

Evaluate the integrals by making appropriate \(u\) -substitutions and applying the formulas reviewed in this section. $$\int \frac{\sec (\ln x) \tan (\ln x)}{x} d x$$

Evaluate the integrals that converge. $$\int_{-\infty}^{0} \frac{d x}{(2 x-1)^{3}}$$

Evaluate the integral. $$\int x \ln x \, d x$$

(a) Use the End paper Integral Table to evaluate the given integral. (b) If you have a CAS, use it to evaluate the integral, and then confirm that the result is equivalent to the one that you found in part (a). $$\int \frac{1}{16-x^{2}} d x$$

Evaluate the integral. $$\int \sin ^{2} t \cos ^{3} t d t$$

Evaluate the integral. $$\int \frac{3 x^{3}}{\sqrt{1-x^{2}}} d x$$

Evaluate the integral. $$\int \frac{d x}{x^{2}-3 x-4}$$

Evaluate the integrals by making appropriate \(u\) -substitutions and applying the formulas reviewed in this section. $$\int e^{\tan x} \sec ^{2} x d x$$

Evaluate the integrals that converge. $$\int_{-\infty}^{3} \frac{d x}{x^{2}+9}$$

Evaluate the integral. $$\int \sqrt{x} \ln x \, d x$$

Evaluate the integral. $$\int \sin ^{3} x \cos ^{2} x d x$$

Evaluate the integral. $$\int x^{3} \sqrt{5-x^{2}} d x$$

Evaluate the integral. $$\int \frac{d x}{x^{2}-6 x-7}$$

Evaluate the integrals by making appropriate \(u\) -substitutions and applying the formulas reviewed in this section. $$\int \frac{x}{\sqrt{1-x^{4}}} d x$$

Evaluate the integrals that converge. $$\int_{-\infty}^{0} e^{3 x} d x$$

(a) Use the End paper Integral Table to evaluate the given integral. (b) If you have a CAS, use it to evaluate the integral, and then confirm that the result is equivalent to the one that you found in part (a). $$\int \sqrt{x^{2}-3} d x$$

Evaluate the integral. $$\int(\ln x)^{2} d x$$

Evaluate the integral. $$\int \sin ^{2} x \cos ^{2} x d x$$

Evaluate the integral. $$\int \frac{d x}{x^{2} \sqrt{9 x^{2}-4}}$$

Evaluate the integral. $$\int \frac{11 x+17}{2 x^{2}+7 x-4} d x$$

Evaluate the integrals by making appropriate \(u\) -substitutions and applying the formulas reviewed in this section. $$\int \cos ^{5} 5 x \sin 5 x d x$$

Evaluate the integrals that converge. $$\int_{-\infty}^{0} \frac{e^{x} d x}{3-2 e^{x}}$$

Evaluate the integral. $$\int \frac{\ln x}{\sqrt{x}} d x$$

Evaluate the integral. $$\int \sin ^{2} x \cos ^{4} x d x$$

Evaluate the integral. $$\int \frac{\sqrt{1+t^{2}}}{t} d t$$

Evaluate the integral. $$\int \frac{5 x-5}{3 x^{2}-8 x-3} d x$$

Evaluate the integrals by making appropriate \(u\) -substitutions and applying the formulas reviewed in this section. $$\int \frac{\cos x}{\sin x \sqrt{\sin ^{2} x+1}} d x$$

Evaluate the integrals that converge. $$\int_{-\infty}^{+\infty} x d x$$

Evaluate the integral. $$\int \ln (3 x-2) d x$$

Evaluate the integral. $$\int \sin 2 x \cos 3 x \, d x$$

Evaluate the integral. $$\int \frac{d x}{\left(1-x^{2}\right)^{3 / 2}}$$

Evaluate the integral. $$\int \frac{2 x^{2}-9 x-9}{x^{3}-9 x} d x$$

Evaluate the integrals by making appropriate \(u\) -substitutions and applying the formulas reviewed in this section. $$\int \frac{e^{x}}{\sqrt{4+e^{2 x}}} d x$$

Evaluate the integral. $$\int \ln \left(x^{2}+4\right) d x$$

(a) Use the End paper Integral Table to evaluate the given integral. (b) If you have a CAS, use it to evaluate the integral, and then confirm that the result is equivalent to the one that you found in part (a). $$\int \frac{1}{x^{2} \sqrt{x^{2}-2}} d x$$

Evaluate the integral. $$\int \sin 3 \theta \cos 2 \theta d \theta$$

Evaluate the integral. $$\int \frac{d x}{x^{2} \sqrt{x^{2}+25}}$$

Evaluate the integral. $$\int \frac{d x}{x\left(x^{2}-1\right)}$$

Evaluate the integrals by making appropriate \(u\) -substitutions and applying the formulas reviewed in this section. $$\int \frac{e^{\tan ^{-1} x}}{1+x^{2}} d x$$

Evaluate the integrals that converge. $$\int_{-\infty}^{+\infty} \frac{x}{\left(x^{2}+3\right)^{2}} d x$$

Evaluate the integral. $$\int \sin ^{-1} x d x$$