Exam 7: Methods of Integration

Integrate $\int \frac{2}{x^{2}+4} d x$

Integrate $\int \cos ^{2} 4 x d x$

Integrate $\int e^{3 x-1} d x$

For the problems below, integrate using a table or a graphing utility. -Find the area within the inner loop of $\mathrm{r}=4+8 \sin \theta$ .

Integrate $\int \frac{4 x}{x^{2}+1} d x$

For the problems below, write each expression as a sum of partial fractions and integrate. - $\int \frac{\left(11 x^{2}-18 x+3\right)}{x(x-1)^{2}} d x$

For the problems below, integrate. - $\int \sec 3 x \tan 3 x d x$

Find the area inside the polar curve $r=2-2 \sin \theta$ .

For the problems below, integrate. - $\int x e^{10 x} d x$

Find the partial fractions of each expression. - $\frac{4 x+36}{(x-3)(x+5)}$

For the problems below, integrate. - $\int \frac{d x}{\sqrt{5-45 x^{2}}}$

For the problems below, integrate. -Evaluate $\int_{2}^{4} \frac{6}{3 x-5} d x$ .

For the problems below, integrate. - $\int \sin 5 x \cos 5 x d x$

For the problems below, integrate. - $\int \sec ^{2}(5 x+10) d x$

For the problems below, integrate. - $\int \frac{(x+1)}{3 x^{2}+6 x} d x$

For the problems below, integrate. - $\int x \ln x d x$

For the problems below, integrate using a table or a graphing utility. -Use Simpson's rule with $n=6$ to find the approximate value of $\int_{1}^{4} \frac{d x}{x+4}$ .

Find the partial fractions of the expression $\frac{5 x^{2}+4 x+4}{x^{3}+2 x^{2}}$ .

Integrate $\int x^{2} \sin x d x$

For the problems below, integrate using a table or a graphing utility. - $\int \frac{d x}{4 x(3+4 x)}$