List of top Mathematics Questions on Integration asked in AP EAPCET

Evaluate \[ \int \frac{1}{(x^4+1)^{5/4}}\,dx. \]

If \[ \int \frac{dx}{2\sin^2x+\sin2x} = \frac12\log|f(x)|+C \] and \[ f\!\left(\frac{\pi}{4}\right)=\frac12, \] then \(f(x)\) is

If \[ \int \frac{2\cos x+3\sin x} {3\cos x+4\sin x}\,dx = Ax+B\log|3\cos x+4\sin x|+C, \] then \[ A\cdot B= \]

If \[ \int 4^x \cdot 4^{4^x}\cdot 4^{\,4^{4^x}}\,dx = A\,4^{\,4^{4^x}}+C, \] then \(A=\)

If \[ \int \frac{dx}{\sin^3x+\cos^3x} = A\log\left| \frac{\sqrt2+t}{\sqrt2-t} \right| + B\tan^{-1}(t)+C, \] then \[ \left(\frac{B}{A},\,t\right) = \]

If \[ \int e^x\frac{x^3+3x^2+4}{(x+1)^3}\,dx = e^x f(x)+C, \] then \(f(x)\) is

If \[ \int (x+5)\sqrt{x-5}\,dx = \frac{2(x-5)^{5/2}}{15}f(x)+c, \] then \(f(6)=\)

Evaluate the integral: \[ \int \frac{x}{x^2-5x+4}\,dx \]

Evaluate: \[ \int \frac{e^{2x}-1}{e^{2x}+e^x+1}\,dx \]

Evaluate: \[ \int \frac{\sin^2 x \cos^2 x}{\cos^6 x+\sin^6 x}\,dx \]

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

Evaluate $\int \frac{x-1}{(x+1)^3}e^x dx$:

If $\int \frac{\cos 8x + 1}{\cot 2x - \tan 2x} dx = A\cos 8x + c$, then $A =$

Evaluate $\int \frac{1+x^2}{\sqrt{1-x^2}} dx$:

The integral \( \int \frac{\cos x - \sin x}{10 + \sin 2x} dx \) is equal to:

The value of the integral \(\int \frac{dx}{\cos 2x + \sin 2x + 2\sin^2 x}\) is:

If \(x > 0\), then \(\int \frac{1}{\sqrt{x^4 + 2x^3 + 2x^2}} dx =\)

The integral \( \int \frac{\cos^3 x}{(1+\sin x)^4} dx \) is equal to:

If \( \int \frac{2x+5}{(x-1)(x+1)(x+4)(x+6)} \, dx = \frac{1}{10}\log\left(\frac{f(x)}{g(x)}\right)+c \) and \( \frac{f(-2)}{g(-2)}=6 \), then \( \frac{f(10)}{g(10)} = \)

If \( \int e^{x}\left(\frac{1}{n}+\tan nx\right)\sec nx \, dx = \frac{1}{n}(g(x)+k) = F(x) \) and \( F(0)=1 \), then \( k = \)

For \( x>0 \), if \( \int \frac{1}{x^{2}+5x+7} \, dx = \frac{2}{\sqrt{3}}F(x)+k \) and \( F\left(-\frac{5}{2}\right)=0 \), then \( \sin(F(x)) = \)

If \( F(x)=\int x(\log x)^{2} \, dx \) and \( F(e)=\frac{e^{2}}{4} \), then \( F(1) = \)

If \( \int e^{5x}x^{n} \, dx = F(n, x) + c \), then \( 5F(n, x) + nF(n-1, x) = \)

If $I_{n}=\int\sin^{n}x dx$, then $I_{6}-\frac{5}{6}I_{4}=$

If $\int\frac{1}{x^{2}+4x+\alpha}dx=\frac{1}{2\sqrt{2}}\tan^{-1}\left(\frac{x+2}{2\sqrt{2}}\right)+c$, then $\int\frac{1}{x^{2}+4x-\alpha}dx=$