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

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

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integral of cos((3x)/2)

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

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

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = \frac{3 x}{2}

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

Add a constant to the solution

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

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

\frac{d}{d x} (2 (x^{^{'}} - n) e^{- (p (x, t) t)})

\frac{d}{d x} (x^{\frac{1}{7}} (x + 8))

\int \frac{1}{x ^{2} x ^{2} - 14} d x

\int_{2}^{3} \frac{1}{3 - x} d x

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