Find $ \displaystyle \displaystyle\int 4 + \sqrt{1-2x} - x^5 - \frac{1}{2x^2} {\rm d}x $ \(\displa

Question

Find $ \displaystyle \displaystyle\int 4 + \sqrt{1-2x} - x^5 - \frac{1}{2x^2} {\rm d}x $ $\displaystyle \displaystyle\int x(x-3)^3 \, {\rm d}x $.

Accepted Answer

(a) $4x-\frac13(1-2x)^{\frac32}-\frac{x^6}{6}+\frac1{2x}+C_1$. (b) $\frac{x^5}{5}-\frac{9x^4}{4}+9x^3-\frac{27x^2}{2}+C_2$.

Indefinite integrals of polynomials and powers