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

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

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integral of sin(2x+3)

\int sin (2 x + 3) d x

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

Solution steps

\int sin (2 x + 3) d x

Apply u-substitution

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

= \int sin (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 sin (u) d u

Use the common integral:

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

= \frac{1}{2} (- cos (u))

Substitute back

u = 2 x + 3

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

Simplify

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

Add a constant to the solution

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

\int_{0}^{1} (x^{2} + 8) e^{- x} d x

y^{^{''}} + 49 y = 0, y (0) = 4, y^{^{''}} (0) = - 6

\int_{0}^{1} 4 (1 + x)^{4} d x

f (x) = 2 x + 2

\frac{\partial}{\partial x} (arctan (x^{2} y))

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