integral of \sqrt[7]{x^2}+xsqrt(x)

解答

\int 7 x^{2} + x x d x

\frac{7}{9} x^{\frac{9}{7}} + \frac{2}{5} x^{\frac{5}{2}} + C

求解步骤

\int 7 x^{2} + x x d x

7 x^{2} = x^{\frac{2}{7}},

假定

x \geq 0

= \int x^{\frac{2}{7}} + x 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^{\frac{2}{7}} d x + \int x x d x

\int x^{\frac{2}{7}} d x = \frac{7}{9} x^{\frac{9}{7}}

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

= \frac{7}{9} x^{\frac{9}{7}} + \frac{2}{5} x^{\frac{5}{2}}

解答补常数

= \frac{7}{9} x^{\frac{9}{7}} + \frac{2}{5} x^{\frac{5}{2}} + C

d er i v a t i v e y = x^{2} + 4 x + 3

n = 0 \sum \infty sin (\frac{1}{n ^{2}})

x \to 0 lim (\frac{\frac{1}{1 + x} - 1}{x})

d er i v a t i v e ln (3 - x^{3})

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