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受欢迎的微积分 >

integral of 14tan^{13}(x)sec^2(x)

解答

\int 14 tan^{13} (x) sec^{2} (x) d x

解答

tan^{14} (x) + C

求解步骤

\int 14 tan^{13} (x) sec^{2} (x) d x

提出常数:

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

= 14 \cdot \int tan^{13} (x) sec^{2} (x) d x

使用三角恒等式改写

= 14 \cdot \int (1 + tan^{2} (x)) tan^{13} (x) d x

使用换元积分法

= 14 \cdot \int u^{13} d u

使用幂法则

= 14 \cdot \frac{u ^{14}}{14}

u = tan (x)

代回

= 14 \cdot \frac{tan ^{14} ( x )}{14}

化简

14 \cdot \frac{tan ^{14} ( x )}{14} : tan^{14} (x)

= tan^{14} (x)

解答补常数

= tan^{14} (x) + C

作图

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