11. Integrals of Inverse, Exponential, & Logarithmic Functions

Evaluate the integral.

${\int }_{}^{}(\frac{2}{\sqrt{1-x^2}}-\frac{1}{3\sqrt{x}})dx$

Evaluate the integral.

${\int }_{\sqrt{2}}^2\frac{1}{\mid x\mid \sqrt{x^2-1}}dx$

Find the indefinite integral.

${\int }_{}^{}\frac{1}{x\sqrt{4x^2-16}}dx$

Evaluate the definite integral in terms of an inverse trig function.

$\int_0^{\frac{\sqrt3}{3}}\frac{dx}{\sqrt{4-9x^2}}$

Evaluate the definite integral using the appropriate substitutions.

${\int }_{\frac{\pi }{2}}^{\pi }\frac{\sin x}{1+co{s}^{2}x}dx$

Find the indefinite integral.

${\int }_{}^{}\frac{arcsi{n}^{4}x}{\sqrt{1-x^2}}dx$

Find the indefinite integral.

${\int }_{}^{}\frac{se{c}^2\left(si{n}^{-1}\theta \right)}{\sqrt{1-{\theta }^2}}d\theta$

Find the indefinite integral.

${\int }_{}^{}\frac{-2}{x^2-12x+45}dx$