What is the integral of-2sin(2x+5) ?

The integral of-2sin(2x+5) is cos(2x+5)+C

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integral of-2sin(2x+5)

\int - 2 sin (2 x + 5) d x

cos (2 x + 5) + C

Solution steps

\int - 2 sin (2 x + 5) d x

Take the constant out:

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

= - 2 \cdot \int sin (2 x + 5) d x

Apply u-substitution

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

= - 2 \cdot \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

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

Use the common integral:

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

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

Substitute back

u = 2 x + 5

= - 2 \cdot \frac{1}{2} (- cos (2 x + 5))

Simplify

- 2 \cdot \frac{1}{2} (- cos (2 x + 5)) : cos (2 x + 5)

= cos (2 x + 5)

Add a constant to the solution

= cos (2 x + 5) + C

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