integral of cos^2(x)x

解答

\int cos^{2} (x) x d x

\frac{1}{2} x (x + \frac{1}{2} sin (2 x)) - \frac{1}{2} (\frac{x ^{2}}{2} - \frac{1}{4} cos (2 x)) + C

求解步骤

\int cos^{2} (x) x d x

使用分布积分法

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

\int \frac{1}{2} (x + \frac{1}{2} sin (2 x)) d x = \frac{1}{2} (\frac{x ^{2}}{2} - \frac{1}{4} cos (2 x))

= \frac{1}{2} x (x + \frac{1}{2} sin (2 x)) - \frac{1}{2} (\frac{x ^{2}}{2} - \frac{1}{4} cos (2 x))

解答补常数

= \frac{1}{2} x (x + \frac{1}{2} sin (2 x)) - \frac{1}{2} (\frac{x ^{2}}{2} - \frac{1}{4} cos (2 x)) + C

t a y l or (\frac{1}{x}), 2

in v erse l a pl a ce \frac{1}{s ^{2} ( s ^{2} + 4 )}

a re a y = 3 x - 6, (2, 4)

\frac{d}{d x} (\frac{2 x ^{3} - 5 x ^{2} + 4 x}{( x - 1 ) ^{2}})

\frac{d}{d x} (\frac{2}{5 x ^{2}})