What is the integral of cos(6-5x) ?

The integral of cos(6-5x) is -1/5 sin(6-5x)+C

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integral of cos(6-5x)

\int cos (6 - 5 x) d x

- \frac{1}{5} sin (6 - 5 x) + C

Solution steps

\int cos (6 - 5 x) d x

Apply u-substitution

: \int - \frac{1}{5} cos (u) d u

= \int - \frac{1}{5} cos (u) d u

Take the constant out:

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

= - \frac{1}{5} \cdot \int cos (u) d u

Use the common integral:

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

= - \frac{1}{5} sin (u)

Substitute back

u = 6 - 5 x

= - \frac{1}{5} sin (6 - 5 x)

Add a constant to the solution

= - \frac{1}{5} sin (6 - 5 x) + C

\int x x + 4 d x

\int \frac{5}{x ^{2} - 25} d x

\int x 5 x + 8 d x

\int (x^{5} - 7 x)^{2} (5 x^{4} - 7) d x

\int \frac{( x ^{2} + 4 x - 8 )}{x ^{2} + 4 x - 5} d x

What is the integral of cos(6-5x) ?
The integral of cos(6-5x) is -1/5 sin(6-5x)+C