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

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\int \frac{12 x ^{2} - 4 x + 7}{3 x + 1} d x

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