What is the integral of cos(5x+2) ?

The integral of cos(5x+2) is 1/5 sin(5x+2)+C

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integral of cos(5x+2)

\int cos (5 x + 2) d x

\frac{1}{5} sin (5 x + 2) + C

Solution steps

\int cos (5 x + 2) d x

Apply u-substitution

: \int cos (u) \frac{1}{5} d u

= \int cos (u) \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{5} sin (u)

Substitute back

u = 5 x + 2

= \frac{1}{5} sin (5 x + 2)

Add a constant to the solution

= \frac{1}{5} sin (5 x + 2) + C

\int \frac{( 2 ln ( x ) + 3 ) ^{3}}{x} d x

\int \frac{3 x ^{2} - 5 x + 1}{x - 4} d x

\int \frac{1}{x + 1 + x} d x

\int \frac{1 0 ^{x}}{x} d x

\int - \frac{4 x + 5}{8 x + 10} d x

What is the integral of cos(5x+2) ?
The integral of cos(5x+2) is 1/5 sin(5x+2)+C