integral of 1/(u^{5/4)}+6.5sqrt(u)

解答

\int \frac{1}{u ^{\frac{5}{4}}} + 6.5 u d u

- \frac{4}{4 u} + 4.33333 \dots u^{\frac{3}{2}} + C

求解步骤

\int \frac{1}{u ^{\frac{5}{4}}} + 6.5 u d u

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{1}{u ^{\frac{5}{4}}} d u + \int 6.5 u d u

\int \frac{1}{u ^{\frac{5}{4}}} d u = - \frac{4}{u ^{\frac{1}{4}}}

\int 6.5 u d u = 4.33333 \dots u^{\frac{3}{2}}

= - \frac{4}{u ^{\frac{1}{4}}} + 4.33333 \dots u^{\frac{3}{2}}

使用根式运算法则:

a^{\frac{1}{n}} = n a

= - \frac{4}{4 u} + 4.33333 \dots u^{\frac{3}{2}}

解答补常数

= - \frac{4}{4 u} + 4.33333 \dots u^{\frac{3}{2}} + C

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