What is the integral of sin(1/5)x ?

The integral of sin(1/5)x is 1/2 sin(1/5)x^2+C

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integral of sin(1/5)x

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

\frac{1}{2} sin (\frac{1}{5}) x^{2} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{2}}{2}

= sin (\frac{1}{5}) \frac{x ^{2}}{2}

Simplify

sin (\frac{1}{5}) \frac{x ^{2}}{2} : \frac{1}{2} sin (\frac{1}{5}) x^{2}

= \frac{1}{2} sin (\frac{1}{5}) x^{2}

Add a constant to the solution

= \frac{1}{2} sin (\frac{1}{5}) x^{2} + C

n = 0 \sum \infty (cos^{2} (5))^{n}

\frac{d x}{d t} = t^{2} e^{x + 2 t}

\frac{d}{d x} (- \frac{1}{x + c})

\frac{d y}{d x} = (y - 1)^{2} x^{3}

y^{^{'}} - 2 y + x^{2} = 0

What is the integral of sin(1/5)x ?
The integral of sin(1/5)x is 1/2 sin(1/5)x^2+C