List of top Mathematics Questions on Integration asked in AP EAPCET

If $\int\frac{2\sin x+a\cos x}{b\sin x+4\cos x}dx=\frac{2}{5}x-\frac{1}{5}\log(b\sin x+4\cos x)+c$, then $a+b=$
If $\int(4\sin\theta+\cos\theta)\cot\theta\cos\theta d\theta=2\theta+\sin2\theta+\log(\sin\theta)+f(2\theta)+c$ and $f(0)=\frac{1}{2}$, then $f(x)=$
The integral $\int \frac{dx}{x(x^4 + 1)} =$
The integral $\int \frac{1}{\cos^2 x (1 - \tan x)^2} \, dx =$
The integral $\int \frac{e^x (1 + x)}{\cos^2(x e^x)} \, dx =$
\(\int \frac{\sqrt{x - 2}}{2x + 4} \, dx =\)
If \( \int x^2 \cos^3 x\, dx = \frac{1}{6}f(x) + g(x) \sin 2x + h(x) \cos 2x + c \), then \( f(1) + g(2) + h\left(\frac{1}{2}\right) = \)
Evaluate: $$ \int_0^1 x \sin^{-1} x \, dx $$
\( \int x \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right) \, dx \, (x>0) = \)
Evaluate the integral: \[ I = \int_{\pi/6}^{\pi/3} \cos^{-4} x \, dx \]
If $$ \int \frac{a \cos x + 3 \sin x}{5 \cos x + 2 \sin x} dx = \frac{26}{29} x - \frac{k}{29} \log |5 \cos x + 2 \sin x| + c, $$ then find $ |a + k| $.
$\int \frac{\sin 2x}{\sin^2 x + 3 \cos x - 3} \, dx =$
Identify the correct option from the following:
If \[ \int \frac{dx}{(x \tan x + 1)^2} = f(x) + c, \] then \(\lim_{x \to \frac{\pi}{2}} f(x)\) is?
\( \int \frac{dx}{12\cos x + 5\sin x} = \)
\( \int \frac{dx}{12\cos x + 5\sin x} = \)
If \(\int \left( \frac{x^{49} \tan^{-1}(x^{50})}{1 + x^{100}} + \frac{x^{50}}{1 + x^{100}} \right) dx = k f(x) + c\) where \(k\) is a constant, then \(f(x) - f\left( \frac{1}{x^{49}} \right) =\)
$\int_0^\pi \frac{x \sin x}{1 + \cos^2 x} \, dx =$
Identify the correct option from the following:
\( \int \frac{13\cos 2x - 9\sin 2x}{3\cos 2x - 4\sin 2x} dx = \)
Evaluate the integral: \[ \int \operatorname{Cos}^{-1} \left( \frac{1-x^2}{1+x^2} \right) dx \]
If \( \int \frac{x}{x \tan x + 1} \, dx = \log f(x) + k \), then \( f\left(\frac{\pi}{4}\right) = \)
If $\int \left[ 3t^2 \sin^{-1} \left( \frac{1}{-t \cos t} \right) \right] \, dt = f(t) \left( \sin^{-1} \left( \frac{1}{t} \right) \right) + c$, then $f(2) =$
Identify the correct option from the following:
Evaluate the integral: \[ I = \int_0^{3\pi/2} \frac{\cos^5 x}{\cos^3 x+\sin^3 x}dx \]
Evaluate \[ \int \frac{x + 1}{(x - 2) \sqrt{1 - x}} \, dx = ? \]
If $ f(x) = \max \{ x^3 - 4, x^4 - 4 \} $ and $ g(x) = \min \{ x^2, x^3 \} $, evaluate: $$ \int_{-1}^1 (f(x) - g(x)) \, dx $$
Evaluate the integral: \[ \int \left[\frac{1}{\cos x} - \frac{1}{\sin x} - \frac{1}{\sin x + 3\cos x}\right] dx \]