What is the integral of 5sin(10x) ?

The integral of 5sin(10x) is -1/2 cos(10x)+C

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integral of 5sin(10x)

\int 5 sin (10 x) d x

- \frac{1}{2} cos (10 x) + C

Solution steps

\int 5 sin (10 x) d x

Take the constant out:

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

= 5 \cdot \int sin (10 x) d x

Apply u-substitution

: \int sin (u) \frac{1}{10} d u

= 5 \cdot \int sin (u) \frac{1}{10} d u

Take the constant out:

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

= 5 \cdot \frac{1}{10} \cdot \int sin (u) d u

Use the common integral:

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

= 5 \cdot \frac{1}{10} (- cos (u))

Substitute back

u = 10 x

= 5 \cdot \frac{1}{10} (- cos (10 x))

Simplify

5 \cdot \frac{1}{10} (- cos (10 x)) : - \frac{1}{2} cos (10 x)

= - \frac{1}{2} cos (10 x)

Add a constant to the solution

= - \frac{1}{2} cos (10 x) + C

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What is the integral of 5sin(10x) ?
The integral of 5sin(10x) is -1/2 cos(10x)+C