What is the integral of cos((5x)/3) ?

The integral of cos((5x)/3) is 3/5 sin((5x)/3)+C

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integral of cos((5x)/3)

\int cos (\frac{5 x}{3}) d x

\frac{3}{5} sin (\frac{5 x}{3}) + C

Solution steps

\int cos (\frac{5 x}{3}) d x

Apply u-substitution

: \int cos (u) \frac{3}{5} d u

= \int cos (u) \frac{3}{5} d u

Take the constant out:

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

= \frac{3}{5} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{3}{5} sin (u)

Substitute back

u = \frac{5 x}{3}

= \frac{3}{5} sin (\frac{5 x}{3})

Add a constant to the solution

= \frac{3}{5} sin (\frac{5 x}{3}) + C

\int_{1}^{2} (3 - \frac{6}{x ^{2}}) d x

f (x) = (1 - 2 x) (1 + 2 x), at x = 2

n = 1 \sum \infty (\frac{3}{8})^{n - 1}

y = \frac{x ^{2} - 2}{2 x + 1}

\int_{0}^{2} x - x^{2} d x

What is the integral of cos((5x)/3) ?
The integral of cos((5x)/3) is 3/5 sin((5x)/3)+C