integral of sec(2w)tan(2w)

解答

\int sec (2 w) tan (2 w) d w

\frac{1}{2} cos (2 w) + \frac{1}{2} sin (2 w) tan (2 w) + C

求解步骤

\int sec (2 w) tan (2 w) d w

使用三角恒等式改写

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

使用分布积分法

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

\int sin (2 w) d w = - \frac{1}{2} cos (2 w)

= - (- \frac{1}{2} cos (2 w)) + \frac{1}{2} sin (2 w) tan (2 w)

化简

= \frac{1}{2} cos (2 w) + \frac{1}{2} sin (2 w) tan (2 w)

解答补常数

= \frac{1}{2} cos (2 w) + \frac{1}{2} sin (2 w) tan (2 w) + C

\int (4 y + 2 x - 5) d x

\int (x^{5} + 1) cos (x^{6} + 6 x) d x

\int \frac{x - 44}{x ^{2} ( x + 4 )} d x

\int (- 2 cos (t)) d t

\int x^{2} + e^{1 - x} d x