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受欢迎的微积分 >

integral of (sin(6x))/(cos^2(6x))

解答

\int \frac{sin ( 6 x )}{cos ^{2} ( 6 x )} d x

解答

\frac{1}{6} sec (6 x) + C

求解步骤

\int \frac{sin ( 6 x )}{cos ^{2} ( 6 x )} d x

使用基本三角恒等式:

\frac{sin ( x )}{cos ( x )} = tan (x)

= \int \frac{tan ( 6 x )}{cos ( 6 x )} d x

使用换元积分法

= \int \frac{tan ( u )}{6 cos ( u )} d u

提出常数:

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

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

使用三角恒等式改写

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

使用换元积分法

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

常数积分:

\int a d x = a x

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

代回

= \frac{1}{6} \cdot 1 \cdot sec (6 x)

化简

= \frac{1}{6} sec (6 x)

解答补常数

= \frac{1}{6} sec (6 x) + C

作图

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