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受欢迎的微积分 >

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

解答

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

解答

- \frac{1}{2} ln ∣ cos (x) ∣ + C

求解步骤

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

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 ( x )}{cos ( x )} d x

使用换元积分法

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

提出常数:

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

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

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} (- ln ∣ u ∣)

u = cos (x)

代回

= \frac{1}{2} (- ln ∣ cos (x) ∣)

化简

= - \frac{1}{2} ln ∣ cos (x) ∣

解答补常数

= - \frac{1}{2} ln ∣ cos (x) ∣ + C

作图

流行的例子

integral of 1/(3t^2)

\int \frac{1}{3 t ^{2}} d t

integral of sqrt(x^2-5x+6)

\int x^{2} - 5 x + 6 d x

integral of ((2x+1))/(2x)

\int \frac{( 2 x + 1 )}{2 x} d x

integral of 1/((1-4x)^{3/2)}

\int \frac{1}{( 1 - 4 x ) ^{\frac{3}{2}}} d x

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

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