What is the integral of-7cos(1/7 x) ?

The integral of-7cos(1/7 x) is -49sin(1/7 x)+C

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integral of-7cos(1/7 x)

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int cos (u) \cdot 7 d u

= - 7 \cdot \int cos (u) \cdot 7 d u

Take the constant out:

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

= - 7 \cdot 7 \cdot \int cos (u) d u

Use the common integral:

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

= - 7 \cdot 7 sin (u)

Substitute back

u = \frac{1}{7} x

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

Simplify

= - 49 sin (\frac{1}{7} x)

Add a constant to the solution

= - 49 sin (\frac{1}{7} x) + C

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What is the integral of-7cos(1/7 x) ?
The integral of-7cos(1/7 x) is -49sin(1/7 x)+C