91Ó°ÊÓ

Simpson's Rule approximations Find the indicated Simpson's Rule approximations to the following integrals. $$\int_{0}^{\pi} \sqrt{\sin x} d x \text { using } n=4 \text { and } n=6 \text { sub-intervals }$$

Evaluate the following integrals or state that they diverge. $$\int_{0}^{\infty} \frac{e^{u}}{e^{2 u}+1} d u$$

Evaluate the following integrals using integration by parts. $$\int x^{2} \sin 2 x d x$$

Evaluate the following integrals. $$\int \frac{\sin x}{\cos ^{2} x+\cos x} d x$$

$$\text {Evaluate the following integrals.}$$ $$\int \frac{3}{(x-1)(x+2)} d x$$

Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table. $$\int \frac{(\ln x) \sin ^{-1}(\ln x)}{x} d x$$

Trigonometric substitutions Evaluate the following integrals using trigonometric substitution. $$\int \frac{d x}{\left(25-x^{2}\right)^{3 / 2}}$$

Evaluate the following integrals using integration by parts. $$\int x^{2} e^{4 x} d x$$

Simpson's Rule approximations Find the indicated Simpson's Rule approximations to the following integrals. $$\int_{4}^{3} \sqrt{x} d x \text { using } n=4 \text { and } n=8 \text { sub- intervals }$$

Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table. $$\int \frac{d t}{\sqrt{1+4 e^{t}}}$$