List of top Mathematics Questions on Integration by Parts asked in AP EAPCET

Evaluate \[ \int x^2(\log x)^2\,dx. \]

If \[ \int \frac{x^2-x+1}{x^2+1}\,e^{\cot^{-1}x}\,dx = A(x)e^{\cot^{-1}x}+C, \] then \(A(x)=\)

If $\int x^5 e^{-4x^3} dx = \frac{1}{48}e^{-4x^3} f(x) + c$, then $f(x) =$

Let \[ f(x)=\int \frac{e^{3x}}{4+8e^{2x}+e^{4x}}\,dx \] and \[ g(x)=\int \frac{2\,dx}{e^{3x}+8e^x+4e^{-x}}, \] then \[ f(x)-g(x)= \] is:

If \[ I_n=\int(\cos^n x+\sin^n x)\,dx \] and \[ I_n-\frac{n-1}{n}I_{n-2} = \frac{\sin x\cos x}{n}f(x), \] then \(f(x)=\)