integral of (x^4)/2-x+2/(x^3)

解答

\int \frac{x ^{4}}{2} - x + \frac{2}{x ^{3}} d x

\frac{x ^{5}}{10} - \frac{x ^{2}}{2} - \frac{1}{x ^{2}} + C

求解步骤

\int \frac{x ^{4}}{2} - x + \frac{2}{x ^{3}} d x

使用积分加法定则:

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

= \int \frac{x ^{4}}{2} d x - \int x d x + \int \frac{2}{x ^{3}} d x

\int \frac{x ^{4}}{2} d x = \frac{x ^{5}}{10}

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

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

= \frac{x ^{5}}{10} - \frac{x ^{2}}{2} - \frac{1}{x ^{2}}

解答补常数

= \frac{x ^{5}}{10} - \frac{x ^{2}}{2} - \frac{1}{x ^{2}} + C

\int \frac{1}{( x ^{2} + 49 ) ^{2}} d x

\int \frac{6 x + 24}{x ^{2} + 8 x - 10} d x

\int arcsec (5 x) d x

\int \frac{- y ^{2}}{2} d y

\int (sin (x))^{7} (cos (x))^{4} d x