integral of x^{1/3}-x^{2/3}

해법

\int x^{\frac{1}{3}} - x^{\frac{2}{3}} d x

\frac{3}{4} x^{\frac{4}{3}} - \frac{3}{5} x^{\frac{5}{3}} + C

솔루션 단계

\int x^{\frac{1}{3}} - x^{\frac{2}{3}} d x

합계 규칙 적용:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{\frac{1}{3}} d x - \int x^{\frac{2}{3}} d x

\int x^{\frac{1}{3}} d x = \frac{3}{4} x^{\frac{4}{3}}

\int x^{\frac{2}{3}} d x = \frac{3}{5} x^{\frac{5}{3}}

= \frac{3}{4} x^{\frac{4}{3}} - \frac{3}{5} x^{\frac{5}{3}}

솔루션에 상수 추가

= \frac{3}{4} x^{\frac{4}{3}} - \frac{3}{5} x^{\frac{5}{3}} + C