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

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

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integral of cos(2-3x)

\int cos (2 - 3 x) d x

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

Solution steps

\int cos (2 - 3 x) d x

Apply u-substitution

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

= \int - \frac{1}{3} cos (u) 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 = 2 - 3 x

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

Add a constant to the solution

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

\frac{d}{d x} (x + \frac{c}{x})

\frac{e ^{t^{2}} - 1}{t}

\int_{6}^{8} \frac{22}{( x - 6 ) ^{3}} d x

\int 7 x + 4 d x

x^{2} y + x + y

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