$Q11)\int \frac{1}{\sqrt{sin^{3}x sin(x+3)}}dx$
$Q12)\int \frac{cos5x+cos4x}{1-2cos3x}dx$
$Q13)\int \frac{1}{1+2sin^{2}x}dx$
$Q14) \int \frac{tanx}{cotx+tanx}dx$
$Q15)\int \frac{sinx}{cotx+tanx}dx$
$Q16)\int \frac{cosx}{cotx+tanx}dx$
$Q17)\int \frac{cosx}{2+3sinx+sin^{2}x}dx$
$Q18)\int \frac{cosx}{1+2sinx+sin^{2}x}dx$
$Q19)\int \sqrt{cotx}dx$
$Q20)\int (\sqrt{cotx}+\sqrt{tanx})dx$
; 06-10-2016 12:59 AM
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[IMG]$\huge {\color{Red} \int (\frac{\tan x}{\cot x+\tan x})dx=\int (\frac{1}{\cot ^{2}x+1})dx =\int \sin ^{2}xdx=1/2[x-1/2\sin 2x]+c}$ [/IMG]
$\huge {\color{Blue} \int (\frac{\sin }{\cot x+\tan x})dx=\int (\frac{\sin x}{\frac{1}{\sin x\cos x}})dx=\int(\sin ^{2}x\cos x)dx=1/3 \sin ^{3}x+c }$
$\huge {\color{Blue}\int (\frac{\cos x}{\tan x+\cos x})dx=\int (\frac{\cos x}{\frac{1}{\sin x\cos x}})dx=\int (\cos ^{2}x)\sin xdx=-1/3\cos ^{3}x+c }$
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