What is the integral of-2sin(2t+7) ?

The integral of-2sin(2t+7) is cos(2t+7)+C

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integral of-2sin(2t+7)

\int - 2 sin (2 t + 7) d t

cos (2 t + 7) + C

Solution steps

\int - 2 sin (2 t + 7) d t

Take the constant out:

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

= - 2 \cdot \int sin (2 t + 7) d t

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 t + 7

= - 2 \cdot \frac{1}{2} (- cos (2 t + 7))

Simplify

- 2 \cdot \frac{1}{2} (- cos (2 t + 7)) : cos (2 t + 7)

= cos (2 t + 7)

Add a constant to the solution

= cos (2 t + 7) + C

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