What is the integral of 5sin(x)cos(x) ?

The integral of 5sin(x)cos(x) is 5/2 sin^2(x)+C

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integral of 5sin(x)cos(x)

\int 5 sin (x) cos (x) d x

\frac{5}{2} sin^{2} (x) + C

Solution steps

\int 5 sin (x) cos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int sin (x) cos (x) d x

Apply u-substitution

: \int u d u

= 5 \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= 5 \cdot \frac{u ^{2}}{2}

Substitute back

u = sin (x)

= 5 \cdot \frac{sin ^{2} ( x )}{2}

Simplify

5 \cdot \frac{sin ^{2} ( x )}{2} : \frac{5}{2} sin^{2} (x)

= \frac{5}{2} sin^{2} (x)

Add a constant to the solution

= \frac{5}{2} sin^{2} (x) + C

\int (- 3 x + 2 x) d x

\int_{2}^{5} (2 - x) (x - 5) d x

\frac{\partial}{\partial x} (1 - \frac{5}{y} + x)

x (3 x - 4)

\int \frac{2}{1 + x ^{2} + y ^{2}} d y

What is the integral of 5sin(x)cos(x) ?
The integral of 5sin(x)cos(x) is 5/2 sin^2(x)+C