What is the integral of cos(3x+4) ?

The integral of cos(3x+4) is 1/3 sin(3x+4)+C

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integral of cos(3x+4)

\int cos (3 x + 4) d x

\frac{1}{3} sin (3 x + 4) + C

Solution steps

\int cos (3 x + 4) 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 + 4

= \frac{1}{3} sin (3 x + 4)

Add a constant to the solution

= \frac{1}{3} sin (3 x + 4) + C

\int \frac{x + ln ( x )}{x} d x

\frac{d}{d x} (\frac{a}{x ^{b}})

x \to - 4 lim (\frac{1}{x ^{2} - 16})

(1 + x^{4}) \frac{d y}{d x} = 2 x^{3} (1 - y^{2})

n = 0 \sum \infty \frac{1}{2 ^{2 n - 1}}

What is the integral of cos(3x+4) ?
The integral of cos(3x+4) is 1/3 sin(3x+4)+C