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

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

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

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

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

Solution steps

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

\frac{( 2 x ^{2} + 16 x + x ^{3^{\frac{1}{2}}} + 5 )}{x ^{3}}

\frac{d ^{2} y}{d x ^{2}} - 2 a \frac{d y}{d x} + a^{2} y = 0

y = x^{4} + 9 x^{2} - x, (1, 9)

\int_{1}^{e} \frac{ln ( z )}{z ^{2}} d z

\frac{d}{d x} (\frac{80}{1 + 0.32 x})

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