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

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

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integral of cos(2x+3)

\int cos (2 x + 3) d x

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

Solution steps

\int cos (2 x + 3) d x

Apply u-substitution

: \int cos (u) \frac{1}{2} d u

= \int cos (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{2} sin (u)

Substitute back

u = 2 x + 3

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

Add a constant to the solution

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

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

\frac{d y}{d t} = \frac{t}{t ^{2} y + y}, y (0) = 7

x \to 7 - lim (∣ x - 7 ∣)

n = 1 \sum \infty \frac{7}{n 8 ^{n}}

\int_{- \infty}^{- 1} \frac{3}{x ^{2}} d x

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