Integrate the function $\frac{2\sin\left(7x\right)^3}{3-3\cos\left(7x\right)^2}$ from 0 to $\frac{\pi }{2}$

Evaluate the integral

$\int_1^2x\ln\left(x\right)dx$

Evaluate the integral

$\int_0^3\sqrt{9-x^2}dx$

Evaluate the integral

$\int_0^1xlnxdx$

Evaluate the integral

$\int_0^1x\ln\left(x\right)dx$

Evaluate the integral

$\int_{-1}^2\frac{3x}{x+4}dx$

Evaluate the integral

$\int_0^1xln\left(x\right)dx$

Evaluate the integral

$\int_9^4\left(\frac{x^2}{x+1}\right)dx$