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受欢迎的微积分 >

integral of 10sec^2(5x)tan(5x)

解答

\int 10 sec^{2} (5 x) tan (5 x) d x

解答

tan^{2} (5 x) + C

求解步骤

\int 10 sec^{2} (5 x) tan (5 x) d x

提出常数:

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

= 10 \cdot \int sec^{2} (5 x) tan (5 x) d x

使用换元积分法

= 10 \cdot \int \frac{u}{5} d u

提出常数:

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

= 10 \cdot \frac{1}{5} \cdot \int u d u

使用幂法则

= 10 \cdot \frac{1}{5} \cdot \frac{u ^{2}}{2}

u = tan (5 x)

代回

= 10 \cdot \frac{1}{5} \cdot \frac{tan ^{2} ( 5 x )}{2}

化简

10 \cdot \frac{1}{5} \cdot \frac{tan ^{2} ( 5 x )}{2} : tan^{2} (5 x)

= tan^{2} (5 x)

解答补常数

= tan^{2} (5 x) + C

作图

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