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

The integral of sin(2*x) is -1/2 cos(2x)+C

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integral of sin(2*x)

\int sin (2 \cdot x) d x

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

Solution steps

\int sin (2 x) d x

Apply u-substitution

: \int sin (u) \frac{1}{2} d u

= \int sin (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= \frac{1}{2} (- cos (u))

Substitute back

u = 2 x

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

Simplify

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

Add a constant to the solution

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

\int 15 - 14 x - x^{2} d x

(y + x^{3} + x y^{2}) d x - (x) d y = 0

\int \frac{18}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

n = 0 \sum \infty \frac{5 ^{n + 1}}{4 ^{n} ( 3 n - 1 ) !}

x \to 4 lim (- \frac{1}{x ^{\frac{3}{2}}})