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受欢迎的微积分 >

integral of arccotan(2x)

解答

\int a rcco tan (2 x) d x

解答

- \frac{1}{2} a c^{2} ro ln ∣ cos (2 x) ∣ + C

求解步骤

\int a rcco tan (2 x) d x

提出常数:

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

= a ccro \cdot \int tan (2 x) d x

化简

a ccro : a c^{2} ro

= a c^{2} ro \cdot \int tan (2 x) d x

使用三角恒等式改写

= a c^{2} ro \cdot \int \frac{sin ( 2 x )}{cos ( 2 x )} d x

使用换元积分法

= a c^{2} ro \cdot \int - \frac{1}{2 u} d u

提出常数:

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

= a c^{2} ro (- \frac{1}{2} \cdot \int \frac{1}{u} d u)

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= a c^{2} ro (- \frac{1}{2} ln ∣ u ∣)

u = cos (2 x)

代回

= a c^{2} ro (- \frac{1}{2} ln ∣ cos (2 x) ∣)

化简

= - \frac{1}{2} a c^{2} ro ln ∣ cos (2 x) ∣

解答补常数

= - \frac{1}{2} a c^{2} ro ln ∣ cos (2 x) ∣ + C

作图

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