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) = \frac{1}{x + 1}, at x = 1

\frac{d}{d x} (\frac{( x + 1 )}{x ^{2} + x + 1})

\int \frac{7}{x ^{2} ( x ^{2} + 25 )} d x

f (x) = e^{- 2 x^{2}}

\frac{d y}{d x} + 20 = 24

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