What is the integral of (1+2sin(x))cos(x) ?

The integral of (1+2sin(x))cos(x) is sin(x)+sin^2(x)+C

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integral of (1+2sin(x))cos(x)

\int (1 + 2 sin (x)) cos (x) d x

sin (x) + sin^{2} (x) + C

Solution steps

\int (1 + 2 sin (x)) cos (x) d x

Expand

(1 + 2 sin (x)) cos (x) : cos (x) + 2 cos (x) sin (x)

= \int cos (x) + 2 cos (x) sin (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 cos (x) d x + \int 2 cos (x) sin (x) d x

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

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

= sin (x) + sin^{2} (x)

Add a constant to the solution

= sin (x) + sin^{2} (x) + C

\int \frac{3}{x ^{2} + x} d x

\int \frac{1}{x ^{3} - x ^{2} - 2 x} d x

\int x^{4} - 1 d x

\int \frac{1}{x x ^{4} - 9} d x

\int x^{2} y^{2} - 3 x d x

What is the integral of (1+2sin(x))cos(x) ?
The integral of (1+2sin(x))cos(x) is sin(x)+sin^2(x)+C