integral of (sin(2x)+5tan^2(x)csc^2(x))

해법

\int (sin (2 x) + 5 tan^{2} (x) csc^{2} (x)) d x

- \frac{1}{2} cos (2 x) + 5 tan (x) + C

솔루션 단계

\int sin (2 x) + 5 tan^{2} (x) csc^{2} (x) d x

합계 규칙 적용:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sin (2 x) d x + \int 5 tan^{2} (x) csc^{2} (x) d x

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

\int 5 tan^{2} (x) csc^{2} (x) d x = 5 tan (x)

= - \frac{1}{2} cos (2 x) + 5 tan (x)

솔루션에 상수 추가

= - \frac{1}{2} cos (2 x) + 5 tan (x) + C