integral of 4x^3-3/(x^4)

해법

\int 4 x^{3} - \frac{3}{x ^{4}} d x

x^{4} + \frac{1}{x ^{3}} + C

솔루션 단계

\int 4 x^{3} - \frac{3}{x ^{4}} 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 4 x^{3} d x - \int \frac{3}{x ^{4}} d x

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

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

= x^{4} - (- \frac{1}{x ^{3}})

단순화

= x^{4} + \frac{1}{x ^{3}}

솔루션에 상수 추가

= x^{4} + \frac{1}{x ^{3}} + C