Question

$intlimits a*x^3(bx^4-c)^n dx$

Answer 1

$int a*x^3(bx^4-c)^ndx=[d(bx^4-c)=4bx^3dxrightarrow dx=frac{d(bx^4-c)}{4bx^3}]=\=int a*x^3(bx^4-c)^nfrac{d(bx^4-c)}{4bx^3}=frac{a}{4b}int(bx^4-c)^nd(bx^4-c)=\=frac{a}{4b}*frac{(bx^4-c)^{n+1}}{n+1}+C$