What is the integral of sin(2x)+5tan^2(x)csc^2(x) ?

The integral of sin(2x)+5tan^2(x)csc^2(x) is -1/2 cos(2x)+5tan(x)+C

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

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

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

Solution steps

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

Apply the Sum Rule:

\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)

Add a constant to the solution

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

\int sec^{2} (x) tan (2 tan (x)) d x

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

\int (5 tan^{2} (x) sec^{2} (x) + 13) d x

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

\int - \frac{6}{7 t 49 t ^{2} - 25} d t

What is the integral of sin(2x)+5tan^2(x)csc^2(x) ?
The integral of sin(2x)+5tan^2(x)csc^2(x) is -1/2 cos(2x)+5tan(x)+C