If $\int \frac{1}{\sqrt{(x-1)(x-2)}}\,dx = \log\left|(x-m)+\sqrt{ax^2+bx+n}\right| + C$ where C is an arbitrary constant and $m,n,a$ and $b$ are constant, then $2m+n+a+b$ is equal to:

$\int_{0}^{1} x^2 e^{x^3} \, dx$ is equal to :

The value of $\int_{-5}^{5} |x + 3| dx$ is

The value of $I = \displaystyle\int (x^3-1)^{1/3}x^5\,dx$ is

If $I_n = \int_{0}^{\pi/4} \tan^n x dx$ then $I_{2024} + I_{2026}$ is equal to:

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

$I=\int_{2}^{8}\frac{\sqrt[3]{x+1}}{\sqrt[3]{x+1}+\sqrt[3]{11-x}}dx$ is equal to :