What is the integral of 11sin^2(x)cos^2(x) ?

The integral of 11sin^2(x)cos^2(x) is 11/8 (x-1/4 sin(4x))+C

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integral of 11sin^2(x)cos^2(x)

\int 11 sin^{2} (x) cos^{2} (x) d x

\frac{11}{8} (x - \frac{1}{4} sin (4 x)) + C

Solution steps

\int 11 sin^{2} (x) cos^{2} (x) d x

Take the constant out:

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

= 11 \cdot \int sin^{2} (x) cos^{2} (x) d x

Rewrite using trig identities

= 11 \cdot \int \frac{1 - cos ( 4 x )}{8} d x

Take the constant out:

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

= 11 \cdot \frac{1}{8} \cdot \int 1 - cos (4 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

= 11 \cdot \frac{1}{8} (\int 1 d x - \int cos (4 x) d x)

\int 1 d x = x

\int cos (4 x) d x = \frac{1}{4} sin (4 x)

= 11 \cdot \frac{1}{8} (x - \frac{1}{4} sin (4 x))

Simplify

11 \cdot \frac{1}{8} (x - \frac{1}{4} sin (4 x)) : \frac{11}{8} (x - \frac{1}{4} sin (4 x))

= \frac{11}{8} (x - \frac{1}{4} sin (4 x))

Add a constant to the solution

= \frac{11}{8} (x - \frac{1}{4} sin (4 x)) + C

\frac{d y}{d x} + (\frac{4}{x}) y = x^{4}

x \to 1 lim (x^{\frac{2}{1 - x}})

\frac{3}{x}, \frac{3}{x ^{2}}, 1, 5

\frac{d}{d x} (\frac{2 x ^{2} - x y + 2 y ^{2}}{x - y})

\int x sin (\frac{1}{5}) x d x

What is the integral of 11sin^2(x)cos^2(x) ?
The integral of 11sin^2(x)cos^2(x) is 11/8 (x-1/4 sin(4x))+C