What is the integral of sin^2(x)+3 ?

The integral of sin^2(x)+3 is 7/2 x-1/4 sin(2x)+C

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integral of sin^2(x)+3

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

\frac{7}{2} x - \frac{1}{4} sin (2 x) + C

Solution steps

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

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

\int 3 d x = 3 x

= \frac{1}{2} (x - \frac{1}{2} sin (2 x)) + 3 x

Simplify

\frac{1}{2} (x - \frac{1}{2} sin (2 x)) + 3 x : \frac{7}{2} x - \frac{1}{4} sin (2 x)

= \frac{7}{2} x - \frac{1}{4} sin (2 x)

Add a constant to the solution

= \frac{7}{2} x - \frac{1}{4} sin (2 x) + C

What is the integral of sin^2(x)+3 ?
The integral of sin^2(x)+3 is 7/2 x-1/4 sin(2x)+C