# Evaluate the integrals using a table of integrals. int x sin^-1 2x dx

Question
Applications of integrals
Evaluate the integrals using a table of integrals.
$$\displaystyle\int{x}{{\sin}^{{-{{1}}}}{2}}{x}{\left.{d}{x}\right.}$$

2021-01-29

### Relevant Questions

Evaluate the integrals.
$$\displaystyle\int{\frac{{{{\sin}^{{-{1}}}{x}}}}{{\sqrt{{{1}-{x}^{{{2}}}}}}}}{\left.{d}{x}\right.}$$
Evaluate the following integrals.
$$\displaystyle\int{\left({2}{x}^{{{3}}}-{x}^{{{2}}}+{3}{x}-{7}\right)}{\left.{d}{x}\right.}$$
Use the table of integrals at the back of the text to evaluate the integrals $$\displaystyle\int{8}{\sin{{\left({4}{t}\right)}}}{\sin{{\left({\frac{{{t}}}{{{2}}}}\right)}}}{\left.{d}{t}\right.}$$
Convert the above indefinite integrals into definate integrals using the intervals $$\displaystyle{\left[{0},{1}\right]}$$.
(a)$$\displaystyle\int\sqrt{{{a}^{{2}}-{x}^{{2}}}}{\left.{d}{x}\right.}$$
(b)$$\displaystyle\int\sqrt{{{1}-{x}^{{2}}}}{\left.{d}{x}\right.}$$
Evaluate the following integrals.
$$\displaystyle\int{\frac{{{\left.{d}{x}\right.}}}{{\sqrt{{{\left({x}-{1}\right)}{\left({3}-{x}\right)}}}}}}$$
Evaluate the following integrals.
$$\displaystyle\int\frac{{{\left.{d}{x}\right.}}}{{\sqrt{{{\left({x}-{1}\right)}{\left({3}-{x}\right)}}}}}$$
$$\displaystyle{\int_{{0}}^{{3}}}\sqrt{{{x}^{{2}}+{16}}}{\left.{d}{x}\right.}$$
$$\displaystyle\int{2}{x}{\left({1}-{x}^{{-{3}}}\right)}{\left.{d}{x}\right.}$$
$$\displaystyle\int\frac{{{\left.{d}{x}\right.}}}{{{x}^{{3}}-{x}^{{2}}}}$$
$$\displaystyle\int{\left(\frac{{x}}{{\sqrt{{{x}-{4}}}}}{\left.{d}{x}\right.}\right.}$$