Chapter 8

Evaluate the integrals in Exercises \(1-28\). $$ \int \frac{d y}{\sqrt{9+y^{2}}} $$

Evaluate the integrals in Exercises \(1-34\) without using tables. $$ \int_{0}^{\infty} \frac{d x}{x^{2}+1} $$

The instructions for the integrals in Exercises \(1-10\) have two parts, one for the Trapezoidal Rule and one for Simpson's Rule. . $$ \int_{1}^{2} x d x $$

Use the table of integrals at the back of the book to evaluate the integrals. \(\int \frac{d x}{x \sqrt{x-3}}\)

Evaluate the integrals in Exercises \(1-14\) $$ \int_{0}^{\pi / 2} \sin ^{5} x d x $$

Expand the quotients in Exercises \(1-8\) by partial fractions. $$ \frac{5 x-13}{(x-3)(x-2)} $$

Evaluate the integrals. \(\int x \sin \frac{x}{2} d x\)

Evaluate each integral in Exercises \(1-36\) by using a substitution to reduce it to standard form. $$ \int \frac{16 x d x}{\sqrt{8 x^{2}+1}} $$

Evaluate the integrals in Exercises \(1-28\). $$ \int \frac{3 d y}{\sqrt{1+9 y^{2}}} $$

Evaluate the integrals in Exercises \(1-34\) without using tables. $$ \int_{1}^{\infty} \frac{d x}{x^{1.001}} $$

The instructions for the integrals in Exercises \(1-10\) have two parts, one for the Trapezoidal Rule and one for Simpson's Rule. . $$ \int_{1}^{3}(2 x-1) d x $$

Use the table of integrals at the back of the book to evaluate the integrals. \(\int \frac{d x}{x \sqrt{x+4}}\)

Evaluate the integrals in Exercises \(1-14\) $$ \int_{0}^{\pi} \sin ^{5} \frac{x}{2} d x $$

Expand the quotients in Exercises \(1-8\) by partial fractions. $$ \frac{5 x-7}{x^{2}-3 x+2} $$

Evaluate the integrals. \(\int \theta \cos \pi \theta d \theta\)

Evaluate each integral in Exercises \(1-36\) by using a substitution to reduce it to standard form. $$ \int \frac{3 \cos x d x}{\sqrt{1+3 \sin x}} $$

Evaluate the integrals in Exercises \(1-28\). $$ \int_{-2}^{2} \frac{d x}{4+x^{2}} $$

The instructions for the integrals in Exercises \(1-10\) have two parts, one for the Trapezoidal Rule and one for Simpson's Rule. . $$ \int_{-1}^{1}\left(x^{2}+1\right) d x $$

Evaluate the integrals in Exercises \(1-34\) without using tables. $$ \int_{0}^{1} \frac{d x}{\sqrt{x}} $$

Use the table of integrals at the back of the book to evaluate the integrals. \(\int \frac{x d x}{\sqrt{x-2}}\)

Evaluate the integrals in Exercises \(1-14\) $$ \int_{-\pi / 2}^{\pi / 2} \cos ^{3} x d x $$

Expand the quotients in Exercises \(1-8\) by partial fractions. $$ \frac{x+4}{(x+1)^{2}} $$

Evaluate the integrals. \(\int t^{2} \cos t d t\)

Evaluate each integral in Exercises \(1-36\) by using a substitution to reduce it to standard form. $$ \int 3 \sqrt{\sin v} \cos v d v $$

Evaluate the integrals in Exercises \(1-28\). $$ \int_{0}^{2} \frac{d x}{8+2 x^{2}} $$

Evaluate the integrals in Exercises \(1-34\) without using tables. $$ \int_{0}^{4} \frac{d x}{\sqrt{4-x}} $$

Use the table of integrals at the back of the book to evaluate the integrals. \(\int \frac{x d x}{(2 x+3)^{3 / 2}}\)

Evaluate the integrals in Exercises \(1-14\) $$ \int_{0}^{\pi / 6} 3 \cos ^{5} 3 x d x $$

The instructions for the integrals in Exercises \(1-10\) have two parts, one for the Trapezoidal Rule and one for Simpson's Rule. . $$ \int_{-2}^{0}\left(x^{2}-1\right) d x $$

Evaluate the integrals. \(\int x^{2} \sin x d x\)

Evaluate each integral in Exercises \(1-36\) by using a substitution to reduce it to standard form. $$ \int \cot ^{3} y \csc ^{2} y d y $$

Evaluate the integrals in Exercises \(1-28\). $$ \int_{0}^{3 / 2} \frac{d x}{\sqrt{9-x^{2}}} $$

The instructions for the integrals in Exercises \(1-10\) have two parts, one for the Trapezoidal Rule and one for Simpson's Rule. . $$ \int_{0}^{2}\left(t^{3}+t\right) d t $$

Evaluate the integrals in Exercises \(1-34\) without using tables. $$ \int_{-1}^{1} \frac{d x}{x^{2 / 3}} $$

Use the table of integrals at the back of the book to evaluate the integrals. \(\int x \sqrt{2 x-3} d x\)

Evaluate the integrals in Exercises \(1-14\) $$ \int_{0}^{\pi / 2} \sin ^{7} y d y $$

Evaluate the integrals. \(\int_{1}^{2} x \ln x d x\)

Evaluate each integral in Exercises \(1-36\) by using a substitution to reduce it to standard form. $$ \int_{0}^{1} \frac{16 x d x}{8 x^{2}+2} $$

Evaluate the integrals in Exercises \(1-28\). $$ \int_{0}^{1 / 2 \sqrt{2}} \frac{2 d x}{\sqrt{1-4 x^{2}}} $$

Use the table of integrals at the back of the book to evaluate the integrals. \(\int x(7 x+5)^{3 / 2} d x\)

Evaluate the integrals in Exercises \(1-14\) $$ \int_{0}^{\pi / 2} 7 \cos ^{7} t d t $$

Evaluate the integrals in Exercises \(1-34\) without using tables. $$ \int_{-8}^{1} \frac{d x}{x^{1 / 3}} $$

Expand the quotients in Exercises \(1-8\) by partial fractions. $$ \frac{z}{z^{3}-z^{2}-6 z} $$

Evaluate the integrals. \(\int_{1}^{e} x^{3} \ln x d x\)

Evaluate each integral in Exercises \(1-36\) by using a substitution to reduce it to standard form. $$ \int_{\pi / 4}^{\pi / 3} \frac{\sec ^{2} z}{\tan z} d z $$

Evaluate the integrals in Exercises \(1-28\). $$ \int \sqrt{25-t^{2}} d t $$

The instructions for the integrals in Exercises \(1-10\) have two parts, one for the Trapezoidal Rule and one for Simpson's Rule. . $$ \int_{1}^{2} \frac{1}{s^{2}} d s $$

Evaluate the integrals in Exercises \(1-34\) without using tables. $$ \int_{0}^{1} \frac{d x}{\sqrt{1-x^{2}}} $$

Use the table of integrals at the back of the book to evaluate the integrals. \(\int \frac{\sqrt{9-4 x}}{x^{2}} d x\)

Evaluate the integrals in Exercises \(1-14\) $$ \int_{0}^{\pi} 8 \sin ^{4} x d x $$