List of top Mathematics Questions on integral asked in AP EAPCET

The value of the integral \( \int_{-2\pi}^{2\pi} \sin^4 x \cos^6 x \, dx \) is equal to:

The value of the integral \( \int_{0}^{\pi/2} \sin^6 x \cos^4 x \, dx \) is equal to:

The value of the integral \( \int_{0}^{32\pi} \sqrt{1 - \cos 4x} \, dx \) is equal to:

The value of the integral \[ \int_{-\frac{\pi}{8092}}^{\frac{\pi}{8092}} \frac{\sec(2023x)}{1 + (2023)^{2023x}} \, dx \] is equal to:

The value of the integral \( \int_{-\frac{\pi}{15}}^{\frac{\pi}{15}} \frac{\cos 5x}{1 + e^{5x}} \, dx \) is equal to:

The integral \[ \int \frac{1}{\sqrt[4]{(x-1)^3(x+2)^5}} \, dx \] is equal to:

The integral $\int \frac{dx}{x(x^4 + 1)} =$

The integral $\int \frac{1}{\cos^2 x (1 - \tan x)^2} \, dx =$

The integral $\int \frac{e^x (1 + x)}{\cos^2(x e^x)} \, dx =$

\(\displaystyle \int \left(\sqrt{x+\sqrt{12x-36}}+\sqrt{x-\sqrt{12x-36}}\right)\,dx=\)

If \(\displaystyle \int \frac{x\,dx}{\sqrt[15]{(1+x^2)^{12}(2+x^2)^{18}}}=\alpha\left(\frac{1+x^2}{2+x^2}\right)^{1/n}+C\), then \(\dfrac{n}{\alpha}=\)

\(\displaystyle \int (\log x)^2 x^3\,dx=\dfrac{x^4}{32}f(x)+C \Rightarrow f(x)=\)

If \(\displaystyle \int \frac{3e^x-7e^{-x}}{7e^x+3e^{-x}}\,dx=Kx+L\log\left(e^{-2x}+\frac{7}{3}\right)+C\), then \(K+L=\)