What is the integral of 12sin(x)cos(x) ?

The integral of 12sin(x)cos(x) is 6sin^2(x)+C

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integral of 12sin(x)cos(x)

\int 12 sin (x) cos (x) d x

6 sin^{2} (x) + C

Solution steps

\int 12 sin (x) cos (x) d x

Take the constant out:

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

= 12 \cdot \int sin (x) cos (x) d x

Apply u-substitution

: \int u d u

= 12 \cdot \int u d u

Apply the Power Rule

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

= 12 \cdot \frac{u ^{2}}{2}

Substitute back

u = sin (x)

= 12 \cdot \frac{sin ^{2} ( x )}{2}

Simplify

12 \cdot \frac{sin ^{2} ( x )}{2} : 6 sin^{2} (x)

= 6 sin^{2} (x)

Add a constant to the solution

= 6 sin^{2} (x) + C

\int \frac{3}{x ^{2} + 3 x - 10} d x

\frac{d y}{d x} + y = e^{2 x}

y = x e^{x^{2}}

\frac{d}{d x} (\frac{3 x - 9}{x + 5})

\int (π - x) \cdot cos (n x) d x

What is the integral of 12sin(x)cos(x) ?
The integral of 12sin(x)cos(x) is 6sin^2(x)+C