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

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

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integral of sin(2)(x)

\int sin (2) (x) d x

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

Solution steps

\int sin (2) x d x

Take the constant out:

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

= sin (2) \cdot \int x d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

x \to 5 lim (sin (\frac{x π}{3}))

\int \frac{x}{3 x ^{2} - 8} d x

\int \frac{1}{4 - 16 x ^{2}} d x

y = e, y = e^{x}, y = e^{- x}

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = 14

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