integral of x^4+8sqrt(x)

解答

\int x^{4} + 8 x d x

\frac{x ^{5}}{5} + \frac{16}{3} x^{\frac{3}{2}} + C

求解步骤

\int x^{4} + 8 x 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 x^{4} d x + \int 8 x d x

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

\int 8 x d x = \frac{16}{3} x^{\frac{3}{2}}

= \frac{x ^{5}}{5} + \frac{16}{3} x^{\frac{3}{2}}

解答补常数

= \frac{x ^{5}}{5} + \frac{16}{3} x^{\frac{3}{2}} + C

\int \frac{x + 1}{2 x + 1} d x

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

\int (x^{1.8} + 7 x^{2.5}) d x

\int (4 u - 6) u^{2} - 3 u d u

\int x (x + 4)^{\frac{1}{4}} d x