What is the integral of 3cos^2(x)sin(2x) ?

The integral of 3cos^2(x)sin(2x) is -3/2 cos^4(x)+C

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integral of 3cos^2(x)sin(2x)

\int 3 cos^{2} (x) sin (2 x) d x

- \frac{3}{2} cos^{4} (x) + C

Solution steps

\int 3 cos^{2} (x) sin (2 x) d x

Take the constant out:

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

= 3 \cdot \int cos^{2} (x) sin (2 x) d x

Apply u-substitution

: \int - u d u

= 3 \cdot \int - u d u

Take the constant out:

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

= 3 (- \int u d u)

Apply the Power Rule

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

= 3 (- \frac{u ^{2}}{2})

Substitute back

u = cos^{2} (x)

= 3 (- \frac{( cos ^{2} ( x ) ) ^{2}}{2})

Simplify

3 (- \frac{( cos ^{2} ( x ) ) ^{2}}{2}) : - \frac{3}{2} cos^{4} (x)

= - \frac{3}{2} cos^{4} (x)

Add a constant to the solution

= - \frac{3}{2} cos^{4} (x) + C

\frac{d}{d x} (8 4 x - 1)

x \to 2 lim (x^{2} + a)

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x

\frac{d}{d x} (cos (ln (x)) + sin (ln (x)))

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

What is the integral of 3cos^2(x)sin(2x) ?
The integral of 3cos^2(x)sin(2x) is -3/2 cos^4(x)+C