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$\int_0^1\left(\frac{ln\left(x\right)}{x}\right)dx$
$\int_0^1xlnxdx$
$\int_0^1x\ln\left(x\right)dx$
$\int_0^1\left(\ln\left(1+x\right)\right)dx$
$\int_1^exlnx\:dx$
$\int_2^3\frac{1}{\sqrt{x-1}}dx$
$\int_0^1\left(\frac{x}{\left(4-x^2\right)^{\frac{3}{2}}}\right)dx$
Integration by parts is an integration method that relates the integral of a product of two or more functions to the integral of their derivative and antiderivative.
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