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)

integral

cos (2 x + 3)

\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

2 x 2 x - 3

\frac{s}{s ^{2} + 9}

\frac{1}{[ ( 1 - x ^{2} ) ( 1 + x ) ]}

\frac{1}{cos ( 2 z ) - 1}

\frac{v + 1}{v ^{2} + 1}

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