$\int_0^{2a} f(x) dx - \int_a^{2a} f(x) dx =$

The value of the integration $\int_{-\pi / 4}^{\pi / 4} (\lambda|\sin x| + \frac{\mu \sin x}{1+\cos x} + \gamma) \, dx$

The value of $ \int_{-3}^{3} (ax^5 + bx^3 + cx + k) dx $,where $a, b, c, k$ are constants,depends only on . . . . . .

Evaluate the integral: $\int_{-4 \pi}^{4 \pi} \tan ^9 x \sin ^6 x \cos ^3 x \, dx$

If $\int_0^{\frac{\pi}{4}} \frac{\sin^2 x}{1+\sin x \cos x} dx = \frac{1}{a} \log_e\left(\frac{a}{3}\right) + \frac{\pi}{b \sqrt{3}}$,where $a, b \in N$,then $a+b$ is equal to ....................

Value of the definite integral $\int_{-3}^{1} (2(t+1)^5 - 5(t+1)^3 + t + 3) dt$ is equal to