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

The integral of cos(3x+2) is 1/3 sin(3x+2)+C

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integral of cos(3x+2)

\int cos (3 x + 2) d x

\frac{1}{3} sin (3 x + 2) + C

Solution steps

\int cos (3 x + 2) d x

Apply u-substitution

: \int cos (u) \frac{1}{3} d u

= \int cos (u) \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{3} sin (u)

Substitute back

u = 3 x + 2

= \frac{1}{3} sin (3 x + 2)

Add a constant to the solution

= \frac{1}{3} sin (3 x + 2) + C

f (x) = 4 (x - \frac{1}{x})^{3}, at x = 2

y = \frac{- 2 x}{x ^{2} + 1}, (0, 0)

f (x) = - \frac{5}{x ^{3}}, y = 0, x = - 4, x = - 1

x \to 0 lim (\frac{x}{csc ^{2} ( x )})

x \to 5 lim (x^{2} - 2 x + 1)

What is the integral of cos(3x+2) ?
The integral of cos(3x+2) is 1/3 sin(3x+2)+C