$\frac{1}{2} \sin x \sqrt{4-9 \sin ^2 x}+\frac{2}{3} \sin ^{-1}\left(\frac{3 \sin x}{2}\right)+c$

$\frac{1}{2} \cos x \sqrt{4-9 \cos ^2 x}+\frac{2}{3} \sin ^{-1}\left(\frac{3 \cos x}{2}\right)+c$

$\frac{1}{2} \sin x \sqrt{4-9 \sin ^2 x}+\frac{2}{3} \cos ^{-1}\left(\frac{3 \cos x}{2}\right)+c$

$\frac{1}{2} \cos x \sqrt{4-9 \sin ^2 x}+\frac{2}{3} \sin ^{-1}\left(\frac{3 \sin x}{2}\right)+c$

$\frac{27}{32}$

$\frac{27}{8}$

$\frac{8}{243}$

$\frac{243}{32}$

$\frac{3}{7} x^7-\frac{2}{5} x^5+\frac{1}{3} x^3-2 x+c$

$\frac{\frac{3}{7} x^7-\frac{2}{5} x^5+\frac{1}{3} x^3-2 x}{\frac{x^3}{3}+x}+c$

$\frac{3}{5} x^5-\frac{5}{3} x^3+6 x-8 \tan ^{-1} x+c$

$\frac{3}{5} x^5-\frac{5}{3} x^3+6 x-8 \sin h^{-1} x+c$

$\frac{1}{2}\left[\sec x-\operatorname{cosec} x-\log \left|\tan \left(\frac{x}{2}\right) \tan \left(\frac{\pi}{4}+\frac{x}{2}\right)\right|\right]+C$

$\sec x-\operatorname{cosec} x+\log \left|\frac{\tan \left(\frac{\pi}{2}\right)}{\tan \left(\frac{\pi}{4}+\frac{x}{2}\right)}\right|+C$

$\frac{1}{2}\left[\sec x-\operatorname{cosec} x-\log \left|\frac{\tan \left(\frac{\pi}{4}+\frac{x}{2}\right)}{\tan \left(\frac{x}{2}\right)}\right|\right]+C$

$\sec x+\operatorname{cosec} x-\log \left|\tan \left(\frac{x}{2}\right)\right|+C$