# Integration by parts and by substitution

## Integration by parts and by substitution

(i) Find

$\int&space;xe^{4x}dx$

(ii) Find

$\int\frac{8}{\left&space;(&space;2x-1&space;\right&space;)^3}dx,&space;\hspace{0.5&space;cm}x>&space;\frac{1}{2}$

(iii) Given that at x=0, solve the differential equation

$\frac{dy}{dx}=e^x\csc&space;2y\csc&space;y$

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