What is the integral of 3sin(x)cos(x) ?

The integral of 3sin(x)cos(x) is 3/2 sin^2(x)+C

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integral of 3sin(x)cos(x)

\int 3 sin (x) cos (x) d x

\frac{3}{2} sin^{2} (x) + C

Solution steps

\int 3 sin (x) cos (x) d x

Take the constant out:

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

= 3 \cdot \int sin (x) cos (x) d x

Apply u-substitution

: \int u d u

= 3 \cdot \int u d u

Apply the Power Rule

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

= 3 \cdot \frac{u ^{2}}{2}

Substitute back

u = sin (x)

= 3 \cdot \frac{sin ^{2} ( x )}{2}

Simplify

3 \cdot \frac{sin ^{2} ( x )}{2} : \frac{3}{2} sin^{2} (x)

= \frac{3}{2} sin^{2} (x)

Add a constant to the solution

= \frac{3}{2} sin^{2} (x) + C

y^{^{''}} + 9 y = \frac{1}{sin ( 3 t )}

y = 2 (x + 1), y = 3 (x + 1), x = 7

\frac{( t + 5 ) 2}{3 ( 2 t ^{2} - 3 ) 3}

\int 2 x - 9 d x

What is the integral of 3sin(x)cos(x) ?
The integral of 3sin(x)cos(x) is 3/2 sin^2(x)+C