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

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

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integral of sin(6-5x)

\int sin (6 - 5 x) d x

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

Solution steps

\int sin (6 - 5 x) d x

Apply u-substitution

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

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

Use the common integral:

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

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

Substitute back

u = 6 - 5 x

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

Simplify

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

Add a constant to the solution

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

\int I n (x + 1) d x

\int x^{\frac{1}{2}} + 9 d x

\int sin (x) \cdot cos^{4} (x) d x

\int (4 x + 5)^{6} d x

\int x^{\frac{1}{2}} + 1 d x

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