Integration strategies - extra practice

(1) $\int x{\sin }^{2}xdx$ (2) $\int x{4}^{x}dx$ (3) $\int x{\sin }^{-1}xdx$

(4) $\int \ln \left(9x^2-1\right)dx$ (5) $\int \frac{\sqrt{9+x^2}}{x}dx$ (6) $\int \frac{\sqrt{1-9x^2}}{x}dx$

(7) $\int \frac{1}{x\sqrt{9x^2-1}}dx$ (8) $\int \frac{x}{\sqrt{9x^2-1}}dx$ (9) $\int \frac{1}{x\sqrt{9x-1}}dx$

(10) $\int \frac{1}{x^2\left(x^2+1\right)}dx$ (11) $\int \frac{1}{x^2\left(x^2-1\right)}dx$ (12) $\int {\tan }^{5}x{\sec }^{4}xdx$

(13) ${\int }_0^{\pi /2}{\cos }^{3}x\sin 2xdx$ (14) $\int \frac{dx}{\sqrt{e^x-1}}$