The value of $\int_{-1}^{2} \frac{|x|}{x} d x$ is

Number of values of $x$ satisfying the equation $\int_{-1}^{x} (8t^2 + \frac{28}{3}t + 4) dt = \frac{(\frac{3}{2})x + 1}{\log_{(x+1)} \sqrt{x+1}}$.

Evaluate the definite integral $\int_{0}^{1} \frac{d x}{\sqrt{1-x^{2}}}$.

The value of the definite integral,$\int\limits_0^{100} {\frac{x}{{{e^{{x^2}}}}}} \,dx$ is equal to

Evaluate the integral: $\int_0^\pi \left(\cos^2 \left(\frac{3\pi}{8} - \frac{x}{4}\right) - \cos^2 \left(\frac{11\pi}{8} + \frac{x}{4}\right)\right) dx$

The integral $\int_{0}^{\frac{\pi}{2}} \frac{1}{3+2 \sin x+\cos x} d x$ is equal to.