Exam 7: Methods of Integration

For the problems below, integrate. - $\int e^{6 x} d x$

Find the partial fractions of each expression. - $\frac{8 \mathrm{x}+10}{(2 \mathrm{x}+5)^{2}}$

For the problems below, integrate. - $\int \frac{\mathrm{x}^{3} \mathrm{dx}}{\sqrt{\mathrm{x}^{2}+25}}$

For the problems below, write each expression as a sum of partial fractions and integrate. - $\int \frac{(8 x-29)}{(x+2)(x-7)} d x$

For the problems below, integrate. - $\int \sin ^{3} 5 x \cos ^{2} 5 x d x$

For the problems below, integrate. - $\int \frac{d x}{\left(49-x^{2}\right)^{3 / 2}}$

For the problems below, integrate. - $\int \tan ^{3} 8 x d x$

For the problems below, integrate. - $\int \frac{d x}{4+25 x^{2}}$

For the problems below, integrate. - $\int \mathrm{x}^{2} \mathrm{e}^{3} d x$

Integrate $\int \frac{\mathrm{dx}}{\left[\sqrt{\mathrm{x}^{2}+9}\right]^{3}}$

Integrate $\int 3 \sin ^{2} x \cos x d x$

Find the partial fractions of each expression. - $\frac{x^{3}+33 x^{2}-12 x+108}{x^{4}-16}$

For the problems below, integrate using a table or a graphing utility. - $\int e^{2 x} \sin 5 x d x$

Integrate $\int \frac{7 x-4}{(x-1)^{2}(x+2)} d x$

Use the following data and Simpson's Rule to approximate the area under the curve. -4 0 4 8 12 16 20 11 9 3 10 21 30 40

For the problems below, integrate. - $\int\left(x^{3}+2 x^{2}\right)^{8}\left(3 x^{2}+4 x\right) d x$