integral of cos(2x)os(x)

解答

\int cos (2 x) d cos (x) d x

d (cos (2 x) sin (x) + \frac{4}{3} sin^{3} (x)) + C

求解步骤

\int cos (2 x) d cos (x) d x

提出常数:

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

= d \cdot \int cos (2 x) cos (x) d x

使用分布积分法

= d (cos (2 x) sin (x) - \int - 2 sin (2 x) sin (x) d x)

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

= d (cos (2 x) sin (x) - (- \frac{4}{3} sin^{3} (x)))

化简

= d (cos (2 x) sin (x) + \frac{4}{3} sin^{3} (x))

解答补常数

= d (cos (2 x) sin (x) + \frac{4}{3} sin^{3} (x)) + C

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

\int \frac{2 x + 4}{x ^{2} + 4 x + 5} d x

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

\int 3 x^{2} sin (x^{3} + 1) d x

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