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

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

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integral of cos(5x+3)

\int cos (5 x + 3) d x

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

Solution steps

\int cos (5 x + 3) d x

Apply u-substitution

: \int cos (u) \frac{1}{5} d u

= \int cos (u) \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{5} sin (u)

Substitute back

u = 5 x + 3

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

Add a constant to the solution

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

f (x) = 10 (1 + 3 x)^{9}, at x = (0)

f (x) = e^{x}, g (x) = 2 - e^{x}, [0, 3]

\frac{d}{d x} (x^{\frac{2}{3}} (x^{2} - 4))

n = 1 \sum \infty \frac{8 ^{n}}{9 ^{n}}

\int_{- \infty}^{- 1} \frac{1}{x ^{3}} d x

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