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

The integral of cos^2(3x)sin^2(3x) is 1/8 (x-1/12 sin(12x))+C

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

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

\frac{1}{8} (x - \frac{1}{12} sin (12 x)) + C

Solution steps

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

Rewrite using trig identities

= \int \frac{1}{8} (1 - cos (12 x)) d x

Take the constant out:

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

= \frac{1}{8} \cdot \int 1 - cos (12 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

= \frac{1}{8} (\int 1 d x - \int cos (12 x) d x)

\int 1 d x = x

\int cos (12 x) d x = \frac{1}{12} sin (12 x)

= \frac{1}{8} (x - \frac{1}{12} sin (12 x))

Add a constant to the solution

= \frac{1}{8} (x - \frac{1}{12} sin (12 x)) + C

x \to 0 lim (x sin (\frac{5}{x}))

y^{^{'}} = \frac{( y + y ^{2} )}{x ^{2}}

\frac{d}{d x} (x^{\frac{3}{4}} y^{3})

\int_{0}^{3} ∣ 3 x - 1 ∣ d x

\frac{\partial}{\partial x} (x^{2} + x y + 3 y)

What is the integral of cos^2(3x)sin^2(3x) ?
The integral of cos^2(3x)sin^2(3x) is 1/8 (x-1/12 sin(12x))+C