antidifferentiation

-> x power -> -1 from power + c

• called antiderivatives / indefinite integrals

$\int 1+42x^{2}dx$

example q: find the antiderivative of $\frac{-2x^5+5x^4}{3x^2}$

• Let $f^{\prime }(x)=\frac{-2x^5+5x^4}{3x^2}=-\frac{2}{3}{x}^3+\frac{5}{3}{x}^2$
• $f(x)=-\frac{1}{6}{x}^4+\frac{5}{9}{x}^3+c$