List of top Mathematics Questions on integral asked in MET

If \( \int f(x)\,dx = g(x) \), then \( \int \cos x \, f(\sin x)\,dx \) is equal to:

\( \int \frac{dx}{\sin x - \cos x + \sqrt{2}} \) is equal to

\( \int \frac{x^2 - 1}{(x^4 + 3x^2 + 1)\tan^{-1}\left(x + \frac{1}{x}\right)} \, dx \) is equal to

\( \int \frac{\cos x}{\sin^2 x (\sin x + \cos x)} \, dx \) is equal to

If \(b<0\), then the roots \(x_1\) and \(x_2\) of the equation \(2x^2 + 6x + b = 0\) satisfy the condition \(\left(\frac{x_1}{x_2}\right) + \left(\frac{x_2}{x_1}\right)<K\), where \(K\) is equal to

If the roots of the equation \((a-1)(x^2 + x + 1)^2 = (a+1)(x^4 + x^2 + 1)\) are real and distinct then the value of \(a \in\)

The value of \[ \int \frac{dx}{x \sqrt{1 - (\log x)^2}} \] is:

The value of \[ \int \frac{x^2}{(x^2 + 2)(x^2 + 3)} \, dx \] is equal to:

The value of \( \int e^{x(\sin x + \cos x)} \, dx \) is:

\( \int \frac{dx}{(x+1)\sqrt{4x+3}} \) is equal to

\( \int \left(\frac{2 - \sin 2x}{1 - \cos 2x}\right) e^{x} \, dx \) is equal to

If \( I_{n} = \int \sin^{n} x \, dx \), then \( n I_{n} - (n-1) I_{n-2} \) equals

The value of \( \int \frac{1}{1 + e^{x}} \, dx \) is:

The value of \( \int \frac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha} \, dx \) is:

The value of \( \int \frac{dx}{x(x^{n} + 1)} \) is:

The value of \( \int e^{x(\sin x + \cos x)} \, dx \) is: