integral of 2ysqrt(y)

解答

\int 2 y y d y

\frac{4}{5} y^{\frac{5}{2}} + C

求解步骤

\int 2 y y d y

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int y y d y

化简

y y : y^{\frac{3}{2}}

= 2 \cdot \int y^{\frac{3}{2}} d y

使用幂法则

= 2 \cdot \frac{2}{5} y^{\frac{5}{2}}

化简

2 \cdot \frac{2}{5} y^{\frac{5}{2}} : \frac{4}{5} y^{\frac{5}{2}}

= \frac{4}{5} y^{\frac{5}{2}}

解答补常数

= \frac{4}{5} y^{\frac{5}{2}} + C

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