What is the integral of-11sin(11x) ?

The integral of-11sin(11x) is cos(11x)+C

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integral of-11sin(11x)

\int - 11 sin (11 x) d x

cos (11 x) + C

Solution steps

\int - 11 sin (11 x) d x

Take the constant out:

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

= - 11 \cdot \int sin (11 x) d x

Apply u-substitution

: \int sin (u) \frac{1}{11} d u

= - 11 \cdot \int sin (u) \frac{1}{11} d u

Take the constant out:

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

= - 11 \cdot \frac{1}{11} \cdot \int sin (u) d u

Use the common integral:

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

= - 11 \cdot \frac{1}{11} (- cos (u))

Substitute back

u = 11 x

= - 11 \cdot \frac{1}{11} (- cos (11 x))

Simplify

- 11 \cdot \frac{1}{11} (- cos (11 x)) : cos (11 x)

= cos (11 x)

Add a constant to the solution

= cos (11 x) + C

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