integral of psqrt(p^2-25)

解答

\int p p^{2} - 25 d p

\frac{1}{3} (p^{2} - 25)^{\frac{3}{2}} + C

求解步骤

\int p p^{2} - 25 d p

使用换元积分法

= \int u^{2} d u

使用幂法则

= \frac{u ^{3}}{3}

u = p^{2} - 25

代回

= \frac{( p ^{2} - 25 ) ^{3}}{3}

化简

\frac{( p ^{2} - 25 ) ^{3}}{3} : \frac{1}{3} (p^{2} - 25)^{\frac{3}{2}}

= \frac{1}{3} (p^{2} - 25)^{\frac{3}{2}}

解答补常数

= \frac{1}{3} (p^{2} - 25)^{\frac{3}{2}} + C

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