91Ó°ÊÓ

Use any method to evaluate the integrals. Most will require trigonometric substitutions, but some can be evaluated by other methods. \(\int \frac{x^{2}}{4+x^{2}} d x\)

Evaluate the integrals using integration by parts. $$\int p^{4} e^{-p} d p$$

Express the integrand as a sum of partial fractions and evaluate the integrals. $$\int \frac{x+3}{2 x^{3}-8 x} d x$$

Estimate the minimum number of subintervals needed to approximate the integrals with an error of magnitude less than \(10^{-4}\) by (a) the Trapezoidal Rule and (b) Simpson's Rule. (The integrals in Exercises \(11-18 \text { are the integrals from Exercises } 1-8 .)\) $$\int_{-1}^{1}\left(t^{3}+1\right) d t$$

Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. $$\int \frac{d \theta}{\sqrt{2 \theta-\theta^{2}}}$$

Evaluate the integrals without using tables. $$\int_{0}^{2} \frac{s+1}{\sqrt{4-s^{2}}} d s$$

Evaluate the integrals. $$\int 7 \cos ^{7} t d t$$

Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. $$\int \frac{\ln y}{y+4 y \ln ^{2} y} d y$$

Use any method to evaluate the integrals. Most will require trigonometric substitutions, but some can be evaluated by other methods. \(\int \frac{x^{3} d x}{\sqrt{x^{2}+4}}\)

Evaluate the integrals without using tables. $$\int_{0}^{\infty} \frac{d x}{(1+x) \sqrt{x}}$$