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

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

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

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

- cos (x) + \frac{sin ^{2} ( x )}{2} + C

Solution steps

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

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

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

= - cos (x) + \frac{sin ^{2} ( x )}{2}

Add a constant to the solution

= - cos (x) + \frac{sin ^{2} ( x )}{2} + C

\int \frac{4 x}{x ^{3} + 1} d x

\int (4 x^{2} + 1)^{3} \cdot 8 x d x

x (1 - x^{2})

x \to 2 lim (x x^{2} - 4)

y^{^{''}} + 5 y^{^{'}} + y = 0

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