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

The integral of cos(3x+5) is 1/3 sin(3x+5)+C

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integral of cos(3x+5)

\int cos (3 x + 5) d x

\frac{1}{3} sin (3 x + 5) + C

Solution steps

\int cos (3 x + 5) 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 + 5

= \frac{1}{3} sin (3 x + 5)

Add a constant to the solution

= \frac{1}{3} sin (3 x + 5) + C

\frac{d}{d t} (2 t)

\frac{\partial}{\partial x} (sin (x) cos (i y))

\int x sin (\frac{1}{x}) d x

\int \frac{2}{2 x} d x

\frac{d}{d t} (2 cos (t) - 2)

What is the integral of cos(3x+5) ?
The integral of cos(3x+5) is 1/3 sin(3x+5)+C