Find the implicit derivative $\frac{d}{dx}\left(x^3-xy+y^2=7\right)$

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

$\int_1^2\left(\frac{1}{x^2}\right)dx$

Evaluate the integral

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

Evaluate the integral

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