Integrals Test ...

The equation $$\displaystyle\int^{\pi/4}_{-\pi/4}\left(a|\sin x|+\dfrac{b\sin x}{1+\cos x}+c\right)dx=0$$, where a, b, c are constants, gives a relation between.

The value of $$\displaystyle\int^{199\pi/2}_{-\pi/2}\sqrt{(1+\cos 2x)}dx$$ is?

Evaluate : $$\displaystyle\int^2_1|x^2-3x+2|dx$$

The value of the integral $$\displaystyle\int^1_0\dfrac{x^{\alpha}-1}{log \alpha}dx$$, is?

Value of $$\displaystyle\int^3_2\dfrac{dx}{\sqrt{(1+x^3)}}$$ is?

The value of $$\int_{1}^{e} \dfrac{1+x^{2} \ln x}{x+x^{2} \ln x} d x$$ is

$$I_{1}=\int_{0}^{\frac{\pi}{2}} \dfrac{\sin x-\cos x}{1+\sin x \cos x} d x, I_{2}=\int_{0}^{2 \pi} \cos ^{6} x d x$$$$I_{3}=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin ^{3} x d x, I_{4}=\int_{0}^{1} \ln \left(\dfrac{1}{x}-1\right) d x,$$ then

If $$\int_{1}^{2} e^{x^{2}} d x=a,$$ then $$\int_{e}^{e^{4}} \sqrt{\ln x} d x$$ is equal to

The value of the definite integral $$\displaystyle \int_{0}^{\pi / 2} \dfrac{\sin 5 x}{\sin x} d x$$ is

If $$\displaystyle \int_{0}^{t} \dfrac{b x \cos 4 x-a \sin 4 x}{x^{2}} d x=\dfrac{a \sin 4 t}{t}-1,$$ where $$0<t<\dfrac{\pi}{4}$$then the values of $$a, b$$ are equal to