List of top Mathematics Questions on Methods of Integration asked in JEE Main

Evaluate the integral $\int_{0}^{1} \frac{1}{\sqrt{3+x} + \sqrt{1+x}} \, dx$ Given that the integral can be expressed in the form $a + b\sqrt{2} + c\sqrt{3}$, where $a, b, c$ are rational numbers, find the value of $2a + 3b - 4c$.

If $\phi(x)=\frac{1}{\sqrt{ x }} \int_{\frac{\pi}{4}}^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) dt , x>$, then $\emptyset^{\prime}\left(\frac{\pi}{4}\right)$ is equal to :

The integral $\int_0^{\frac{\pi}{2}} \frac{1}{3 + 2\sin x + \cos x} \, dx$ is equal to

The value of $\int \limits \frac {dx}{x^2(x^4+1)^{3/4}}$ is

The integral $\int^{^{\frac{1}{2}}}_{_0} \frac{ln \left(1+2x\right)}{1+4x^{2}}dx,$ equals :