91Ó°ÊÓ

For the following exercises, evaluate the integral using the specified method. \(\int \frac{x^{5}}{\left(4 x^{2}+4\right)^{5 / 2}} d x\) using trigonometric substitution

For the following exercises, evaluate the integral using the specified method. \(\int \frac{\sqrt{4-\sin ^{2}(x)}}{\sin ^{2}(x)} \cos (x) d x\) using a table of integrals or a CAS

For the following exercises, integrate using whatever method you choose. $$ \int \sin ^{2}(x) \cos ^{2}(x) d x $$

For the following exercises, integrate using whatever method you choose. $$ \int x^{3} \sqrt{x^{2}+2} d x $$

For the following exercises, integrate using whatever method you choose. $$ \int \frac{3 x^{2}+1}{x^{4}-2 x^{3}-x^{2}+2 x} d x $$

For the following exercises, integrate using whatever method you choose. $$ \int \frac{1}{x^{4}+4} d x $$

For the following exercises, integrate using whatever method you choose. $$ \int \frac{\sqrt{3+16 x^{4}}}{x^{4}} d x $$

For the following exercises, approximate the integrals using the midpoint rule, trapezoidal rule, and Simpson's rule using four subintervals, rounding to three decimals. $$ [\mathrm{T}] \int_{1}^{2} \sqrt{x^{5}+2} d x $$

For the following exercises, approximate the integrals using the midpoint rule, trapezoidal rule, and Simpson's rule using four subintervals, rounding to three decimals. $$ [\mathbf{T}] \int_{0}^{\sqrt{\pi}} e^{-\sin \left(x^{2}\right)} d x $$

For the following exercises, approximate the integrals using the midpoint rule, trapezoidal rule, and Simpson's rule using four subintervals, rounding to three decimals. $$ [\mathrm{T}] \int_{1}^{4} \frac{\ln (1 / x)}{x} d x $$