integral of (2cos(x))/(3sin^2(x))

解答

\int \frac{2 cos ( x )}{3 sin ^{2} ( x )} d x

- \frac{2}{3} csc (x) + C

求解步骤

\int \frac{2 cos ( x )}{3 sin ^{2} ( x )} d x

提出常数:

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

= \frac{2}{3} \cdot \int \frac{cos ( x )}{sin ^{2} ( x )} d x

使用换元积分法

= \frac{2}{3} \cdot \int \frac{1}{u ^{2}} d u

使用幂法则

= \frac{2}{3} (- \frac{1}{u})

u = sin (x)

代回

= \frac{2}{3} (- \frac{1}{sin ( x )})

化简

\frac{2}{3} (- \frac{1}{sin ( x )}) : - \frac{2}{3} csc (x)

= - \frac{2}{3} csc (x)

解答补常数

= - \frac{2}{3} csc (x) + C

\int_{1}^{2} (4 x^{3} - 3 x^{2} + 2 x) d x

\int cos (3 x - 1) d x

\int (3 t e^{t}, ln (t)) d t

\int \frac{3 x ^{2}}{2} - x - 16.5 d x

2 x^{3} \frac{d y}{d x} = y (2 x^{2} - y^{2})