What is the integral of cos(2x+1) ?

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

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integral of cos(2x+1)

\int cos (2 x + 1) d x

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

Solution steps

\int cos (2 x + 1) 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 + 1

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

Add a constant to the solution

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

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

\int_{- 2}^{0} x 4 - x^{2} d x

\int_{7}^{\infty} \frac{1}{x ^{2} + x} d x

\int 2 x x^{2} - 4 d x

f (x) = \frac{1}{x}, [1, 3]

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