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受欢迎的微积分 >

integral of 5sec(3x^2+4)tan(3x^2+4)x

解答

\int 5 sec (3 x^{2} + 4) tan (3 x^{2} + 4) x d x

解答

\frac{5}{6} sec (3 x^{2} + 4) + C

求解步骤

\int 5 sec (3 x^{2} + 4) tan (3 x^{2} + 4) x d x

提出常数:

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

= 5 \cdot \int sec (3 x^{2} + 4) tan (3 x^{2} + 4) x d x

使用换元积分法

= 5 \cdot \int \frac{sec ( u ) tan ( u )}{6} d u

提出常数:

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

= 5 \cdot \frac{1}{6} \cdot \int sec (u) tan (u) d u

使用换元积分法

= 5 \cdot \frac{1}{6} \cdot \int 1 d v

常数积分:

\int a d x = a x

= 5 \cdot \frac{1}{6} \cdot 1 \cdot v

代回

= 5 \cdot \frac{1}{6} \cdot 1 \cdot sec (3 x^{2} + 4)

化简

5 \cdot \frac{1}{6} \cdot 1 \cdot sec (3 x^{2} + 4) : \frac{5}{6} sec (3 x^{2} + 4)

= \frac{5}{6} sec (3 x^{2} + 4)

解答补常数

= \frac{5}{6} sec (3 x^{2} + 4) + C

作图

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