List of top Mathematics Questions on Methods of Integration asked in KEAM

\[ \int \left(27x^3(1-x^3)\right)^{\frac{2}{3}}\,dx = \]

\(\int \frac{\sec x \sqrt{\sec x}}{\sqrt{\sin x} + \sqrt{\cos x}} dx = \)

If $\int \frac{5\sqrt{x}(4x^2 - 1)}{x} dx = 8\sqrt{x^5} + a\sqrt{x} + C$, where $a$ is a constant and $C$ is the constant of integration, then the value of $a$ is

$\int \frac{\sqrt{\sqrt{x} + 1}}{\sqrt{x}} dx = $}

$\int\frac{\log(1+x)}{(1+x)}dx=$ ________.

$\int\frac{\cos \theta}{2-\sin^{2}\theta}d \theta=$ ________.

$\int e^{x}[\frac{1}{1+x}-\frac{1}{(1+x)^{2}}]dx=$ ________.

$\int \frac{1}{x^2}(x^4 + 1)^{3/4} \, dx$ is equal to:

\( \int \frac{(1 + x) e^x{\sin^2}(x e^x)} dx \) is equal to:

$\int \frac{x e^x}{(1+x)^2} \, dx$ is equal to:

\( \int e^x (\sin x + 2 \cos x) \sin x \, dx \) is equal to:

\( \int \sqrt{1 + \cos x} \, dx \) is equal to:

\( \int \frac{\sqrt{x^2 - 1}}{x} \, dx \) is equal to:

\( \int e^x (\sin x + 2 \cos x) \sin x \, dx \) is equal to:

\( \int \sqrt{1 + \cos x} \, dx \) is equal to:

\( \int \frac{\sqrt{x^2 - 1}}{x} \, dx \) is equal to:

\( \int \frac{1}{x^2 (x^4 + 1)^{3/4 dx \) is equal to:}

\( \int \frac{(1 + x) e^x{\sin^2(x e^x)} dx \) is equal to:}

\( \int \frac{xe^x}{(1+x)^2 \, dx \) is equal to:}

\( \int \frac{(1 + x) e^x{\sin^2(x e^x)} dx \) is equal to:}

\( \int \frac{xe^x}{(1+x)^2 \, dx \) is equal to:}

\( \int e^x (\sin x + 2 \cos x) \sin x \, dx \) is equal to:

\( \int \sqrt{1 + \cos x} \, dx \) is equal to:

\( \int \frac{\sqrt{x^2 - 1}}{x} \, dx \) is equal to:

\( \int \frac{1}{x^2 (x^4 + 1)^{3/4 dx \) is equal to:}