List of top Mathematics Questions on Methods of Integration asked in AP EAPCET

If \[ \int \frac{\tan x}{1+\tan x+\tan^2x}\,dx = x-\frac{K}{\sqrt A} \tan^{-1} \left( \frac{K\tan x+1}{\sqrt A} \right) +C, \] then the ordered pair \((K,A)\) is

Evaluate \[ \int \frac{dx}{(1+\sqrt{x})\sqrt{x-x^2}}. \]

Evaluate \[ \int \sqrt{1+2\cot x(\cot x+\cosec x)}\,dx \]

Evaluate \[ \int \frac{\cos^4x}{\left(\sin^2x+\sin^{-3}x\cos^5x\right)^3}\,dx \]

If \[ \int \frac{\sin^3x\left(\tan^{-1}(\sec x+\cos x)\right)^{-1}}{\cos^4x+3\cos^2x+1}\,dx=f(x)+C, \] then \[ e^{f(x)}= \]

Evaluate \[ \int \frac{1}{\left(\sin x+\cos x+\sqrt{2\sin 2x}\right)^2}\,dx= \]

There exists \(\theta\) such that \[ a\gt |\sec\theta|, \] then \[ \int \frac{dx}{1+a\cos x} = \] is:

Evaluate \[ \int \frac{x^2}{x^3\sqrt{x^2-1}}\,dx = \]

Evaluate \[ \int \frac{e^{\tan^{-1}x}}{1+x^2} \left[ \left(\sec^{-1}\sqrt{1+x^2}\right)^2+ \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right) \right]dx \]

Evaluate \[ \int \frac{dx}{(x-3)^{4/5}(x+1)^{6/5}} \]