91Ó°ÊÓ

Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. $$\int \frac{d x}{e^{x}\left(3 e^{x}+2\right)}$$

\(7-34=\) Evaluate the integral. $$\int_{0}^{1} \frac{x}{x^{2}+4 x+13} d x$$

Evaluate the integral. \(\int_{\pi / 6}^{\pi / 2} \cot ^{2} x d x\)

\(7-34=\) Evaluate the integral. $$\int \frac{1}{x^{3}-1} d x$$

Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. $$\int \cos ^{4} x d x$$

First make a substitution and then use integration by parts to evaluate the integral. $$ \int_{\sqrt{\pi / 2}}^{\sqrt{\pi}} \theta^{3} \cos \left(\theta^{2}\right) d \theta $$

Determine whether each integral is convergent or divergent. Evaluate those that are convergent. $$\int_{0}^{1} \frac{d x}{\sqrt{1-x^{2}}}$$

First make a substitution and then use integration by parts to evaluate the integral. $$ \int_{1}^{4} e^{\sqrt{x}} d x $$

\(7-34=\) Evaluate the integral. $$\int \frac{x^{5}+x-1}{x^{3}+1} d x$$

(a) A table of values of a function \(g\) is given. Use Simpson's Rule to estimate \(\int_{0}^{1.6} g(x) d x\) (b) If \(-5 \leqslant g^{(4)}(x) \leqslant 2\) for \(0 \leqslant x \leqslant 1.6,\) estimate the error involved in the approximation in part (a).