What is the integral of cos((2x)/3) ?

The integral of cos((2x)/3) is 3/2 sin((2x)/3)+C

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integral of cos((2x)/3)

\int cos (\frac{2 x}{3}) d x

\frac{3}{2} sin (\frac{2 x}{3}) + C

Solution steps

\int cos (\frac{2 x}{3}) d x

Apply u-substitution

: \int cos (u) \frac{3}{2} d u

= \int cos (u) \frac{3}{2} d u

Take the constant out:

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

= \frac{3}{2} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{3}{2} sin (u)

Substitute back

u = \frac{2 x}{3}

= \frac{3}{2} sin (\frac{2 x}{3})

Add a constant to the solution

= \frac{3}{2} sin (\frac{2 x}{3}) + C

\int_{0}^{1} - 3 x 5^{x} d x

\frac{d}{d x} (ln (7 x^{5}))

\frac{d}{d x} (\frac{x e ^{x} - 9 x}{e ^{x}})

9 x^{- 4} - 9 x^{- 1}

\int_{- \infty}^{1} 5^{x} d x

What is the integral of cos((2x)/3) ?
The integral of cos((2x)/3) is 3/2 sin((2x)/3)+C