Question

int (x^3dx)/((5x^4+3)^5) int (e^6x^2 xdx)

Answer 1

$1); ; int frac{x^3, dx}{(5x^4+3)^5} =[; t=5x^4+3; ,; dt=20x^3, dx; ]=\\= frac{1}{20}int frac{dt}{t^5} = frac{1}{20}cdot frac{t^{-4}}{-4} +C=- frac{1}{80cdot (5x^4+3)^4} +C\\2); ; int ; e^{6x^2}cdot x, dx=[; t=6x^2; ,; dt=12x, dx; ]=\\= frac{1}{12} cdot int ; e^{t}, dt= frac{1}{12} cdot e^{t}+C= frac{1}{12} cdot e^{6x^2}+C$