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受欢迎的微积分 >

integral of (sin(2x))/(sqrt(cos(2x)))

解答

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

解答

- cos (2 x) + C

求解步骤

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

使用换元积分法

= \int \frac{sin ( u )}{2 cos ( u )} d u

提出常数:

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

= \frac{1}{2} \cdot \int \frac{sin ( u )}{cos ( u )} d u

使用换元积分法

= \frac{1}{2} \cdot \int - \frac{1}{v} d v

提出常数:

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

= \frac{1}{2} (- \int \frac{1}{v} d v)

使用幂法则

= \frac{1}{2} (- 2 v^{\frac{1}{2}})

代回

= \frac{1}{2} (- 2 cos^{\frac{1}{2}} (2 x))

化简

\frac{1}{2} (- 2 cos^{\frac{1}{2}} (2 x)) : - cos (2 x)

= - cos (2 x)

解答补常数

= - cos (2 x) + C

作图

流行的例子

integral of (x^2)/((1-x)^{100)}

\int \frac{x ^{2}}{( 1 - x ) ^{100}} d x

integral of xln((1+x)/(1-x))

\int x ln (\frac{1 + x}{1 - x}) d x

integral of e^{2x}arctan(sqrt(e^x-1))

\int e^{2 x} arctan (e^{x} - 1) d x

integral of sin^2(x)tan(x)

\int sin^{2} (x) tan (x) d x

integral of 1/(x^2-8x+25)

\int \frac{1}{x ^{2} - 8 x + 25} d x