What is the integral of 6e^{6s}sin(e^{6s}) ?

The integral of 6e^{6s}sin(e^{6s}) is -cos(e^{6s})+C

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integral of 6e^{6s}sin(e^{6s})

\int 6 e^{6 s} sin (e^{6 s}) d s

- cos (e^{6 s}) + C

Solution steps

\int 6 e^{6 s} sin (e^{6 s}) d s

Take the constant out:

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

= 6 \cdot \int e^{6 s} sin (e^{6 s}) d s

Apply u-substitution

: \int \frac{sin ( u )}{6} d u

= 6 \cdot \int \frac{sin ( u )}{6} d u

Take the constant out:

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

= 6 \cdot \frac{1}{6} \cdot \int sin (u) d u

Use the common integral:

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

= 6 \cdot \frac{1}{6} (- cos (u))

Substitute back

u = e^{6 s}

= 6 \cdot \frac{1}{6} (- cos (e^{6 s}))

Simplify

6 \cdot \frac{1}{6} (- cos (e^{6 s})) : - cos (e^{6 s})

= - cos (e^{6 s})

Add a constant to the solution

= - cos (e^{6 s}) + C

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What is the integral of 6e^{6s}sin(e^{6s}) ?
The integral of 6e^{6s}sin(e^{6s}) is -cos(e^{6s})+C