What is the integral of cos(4x+5) ?

The integral of cos(4x+5) is 1/4 sin(4x+5)+C

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integral of cos(4x+5)

\int cos (4 x + 5) d x

\frac{1}{4} sin (4 x + 5) + C

Solution steps

\int cos (4 x + 5) d x

Apply u-substitution

: \int cos (u) \frac{1}{4} d u

= \int cos (u) \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{4} sin (u)

Substitute back

u = 4 x + 5

= \frac{1}{4} sin (4 x + 5)

Add a constant to the solution

= \frac{1}{4} sin (4 x + 5) + C

\int (\frac{2 x}{x ^{2} - 36} + \frac{1}{x} + 7) d x

\int c

\frac{d y}{d x} = - 3 y^{\frac{2}{3}} sin (x)

x \to - \infty lim (\frac{3}{x})

\frac{d}{d x} (\frac{1}{2} ln (\frac{x + 1}{x + 3}))

What is the integral of cos(4x+5) ?
The integral of cos(4x+5) is 1/4 sin(4x+5)+C