What is the integral of-cos(7x) ?

The integral of-cos(7x) is -1/7 sin(7x)+C

integral of-cos(7x)

\int - cos (7 x) d x

- \frac{1}{7} sin (7 x) + C

Solution steps

\int - cos (7 x) d x

Take the constant out:

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

= - \int cos (7 x) d x

Apply u-substitution

= - \int cos (u) \frac{1}{7} d u

Take the constant out:

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

= - \frac{1}{7} \cdot \int cos (u) d u

Use the common integral:

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

= - \frac{1}{7} sin (u)

Substitute back

u = 7 x

= - \frac{1}{7} sin (7 x)

Add a constant to the solution

= - \frac{1}{7} sin (7 x) + C

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