What is the integral of sin^2(14x) ?

The integral of sin^2(14x) is 1/2 (x-1/28 sin(28x))+C

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integral of sin^2(14x)

\int sin^{2} (14 x) d x

\frac{1}{2} (x - \frac{1}{28} sin (28 x)) + C

Solution steps

\int sin^{2} (14 x) d x

Rewrite using trig identities

= \int \frac{1}{2} (1 - cos (28 x)) d x

Take the constant out:

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

= \frac{1}{2} \cdot \int 1 - cos (28 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}{2} (\int 1 d x - \int cos (28 x) d x)

\int 1 d x = x

\int cos (28 x) d x = \frac{1}{28} sin (28 x)

= \frac{1}{2} (x - \frac{1}{28} sin (28 x))

Add a constant to the solution

= \frac{1}{2} (x - \frac{1}{28} sin (28 x)) + C

\frac{d y}{d x} = - 5 - 5 x + y

2 y d x + x^{2} d y = - d x

\int x^{2} 3^{5 x^{3} + 1} d x

\int_{0}^{\frac{1}{2}} x^{2} d x

\int 2 y d y

What is the integral of sin^2(14x) ?
The integral of sin^2(14x) is 1/2 (x-1/28 sin(28x))+C