integral of 1/(x^2)sin(x)

解答

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

- \frac{sin ( x )}{x} + Ci (x) + C

求解步骤

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

化简

\frac{1}{x ^{2}} sin (x) : \frac{sin ( x )}{x ^{2}}

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

使用分布积分法

= - \frac{sin ( x )}{x} - \int - \frac{cos ( x )}{x} d x

\int - \frac{cos ( x )}{x} d x = - Ci (x)

= - \frac{sin ( x )}{x} - (- Ci (x))

化简

= - \frac{sin ( x )}{x} + Ci (x)

解答补常数

= - \frac{sin ( x )}{x} + Ci (x) + C

\int (2 x + 3) (2 x - 1) d x

\int \frac{1}{x ^{\frac{1}{3}} + x} d x

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

\int x^{5} e^{- x^{4}} d x

\int \frac{sec ^{2} ( arctan ( 2 x ) )}{1 + 4 x ^{2}} d x