Integration strategies - extra practice

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

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

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

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

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