What is the integral of (4sin(x)+2csc^2(x)+4) ?

The integral of (4sin(x)+2csc^2(x)+4) is -4cos(x)-2cot(x)+4x+C

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integral of (4sin(x)+2csc^2(x)+4)

\int (4 sin (x) + 2 csc^{2} (x) + 4) d x

- 4 cos (x) - 2 cot (x) + 4 x + C

Solution steps

\int 4 sin (x) + 2 csc^{2} (x) + 4 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 4 sin (x) d x + \int 2 csc^{2} (x) d x + \int 4 d x

\int 4 sin (x) d x = - 4 cos (x)

\int 2 csc^{2} (x) d x = - 2 cot (x)

\int 4 d x = 4 x

= - 4 cos (x) - 2 cot (x) + 4 x

Add a constant to the solution

= - 4 cos (x) - 2 cot (x) + 4 x + C

\int 1 - 4 x d x

\int \frac{50 x + 10 x ^{3}}{10 x ^{2} + x ^{4}} d x

\int sin^{2} (10 x) cos^{3} (10 x) d x

\int - 2 z d z

\int (3^{x})^{3} d x

What is the integral of (4sin(x)+2csc^2(x)+4) ?
The integral of (4sin(x)+2csc^2(x)+4) is -4cos(x)-2cot(x)+4x+C