List of top Mathematics Questions on Integration

Find: \[ \int \frac{e^{4x} - 1}{e^{4x} + 1} \, dx. \]

Find: \[ \int \frac{(3 \cos x - 2) \sin x}{5 - \sin^2 x - 4 \cos x} \, dx. \]

The integral $ \int (3x^2 - 2x + 1) \, dx $ is:

The number of points of discontinuity of \( f(x) = \begin{cases} |x| + 3, & \text{if } x \leq -3, \\ -2x, & \text{if } -3 < x < 3, \\ 6x + 2, & \text{if } x \geq 3 \end{cases} \) is:

Find: \[ \int \frac{e^{4x} - 1}{e^{4x} + 1} \, dx. \]

Find: \[ \int x^2 \log(x^2 - 1) \, dx. \]

Evaluate: \[ \int_{-2}^{2} \sqrt{\frac{2 - x}{2 + x}} \, dx. \]

Find: \[ \int \frac{1}{x \left[(\log x)^2 - 3 \log x - 4\right]} \, dx. \]

The anti-derivative of \( \sqrt{1 + \sin 2x}, \, x \in \left[ 0, \frac{\pi}{4} \right] \) is:

If \( M \) and \( m \) denote the local maximum and local minimum values of the function \( f(x) = x + \frac{1}{x} \) (\( x \neq 0 \)) respectively, find the value of \( M - m \).

Find: \[ \int \frac{1}{x \left[(\log x)^2 - 3 \log x - 4\right]} \, dx. \]

Find: \[ \int x^2 \sin^{-1}(x^{3/2}) \, dx. \]

Evaluate: \[ \int_0^a \frac{x^2}{x^6 + a^6} \, dx \]

If \[ \int_0^2 2e^{2x} \, dx = \int_0^a e^x \, dx, \text{ the value of 'a' is:} \]

Find: \[ \int x^2 \sin^{-1}(x^{3/2}) \, dx. \]

Find: \[ \int \frac{1}{x \left[(\log x)^2 - 3 \log x - 4\right]} \, dx. \]

Evaluate: \[ \int_{-2}^{2} \sqrt{\frac{2 - x}{2 + x}} \, dx. \]

Using integration, find the area of the ellipse: \[ \frac{x^2}{16} + \frac{y^2}{4} = 1, \] included between the lines \(x = -2\) and \(x = 2\).

Find: \[ \int \frac{x^2}{(x^2 + 4)(x^2 + 9)} \, dx. \]

Find: \[ \int x \sqrt{1 + 2x} \, dx \]

\(\int\limits_1^5(|x-3|+|1-x|)dx\)=