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

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

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integral of 7cos(7x)

\int 7 cos (7 x) d x

sin (7 x) + C

Solution steps

\int 7 cos (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 (7 x) d x

Apply u-substitution

= 7 \cdot \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

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

Use the common integral:

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

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

Substitute back

u = 7 x

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

Simplify

7 \cdot \frac{1}{7} sin (7 x) : sin (7 x)

= sin (7 x)

Add a constant to the solution

= sin (7 x) + C