What is the integral of e^{3x}sin(7k) ?

The integral of e^{3x}sin(7k) is sin(7k) 1/3 e^{3x}+C

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integral of e^{3x}sin(7k)

\int e^{3 x} sin (7 k) d x

sin (7 k) \frac{1}{3} e^{3 x} + C

Solution steps

\int e^{3 x} sin (7 k) d x

Take the constant out:

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

= sin (7 k) \cdot \int e^{3 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{3} d u

= sin (7 k) \cdot \int e^{u} \frac{1}{3} d u

Take the constant out:

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

= sin (7 k) \frac{1}{3} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= sin (7 k) \frac{1}{3} e^{u}

Substitute back

u = 3 x

= sin (7 k) \frac{1}{3} e^{3 x}

Add a constant to the solution

= sin (7 k) \frac{1}{3} e^{3 x} + C

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What is the integral of e^{3x}sin(7k) ?
The integral of e^{3x}sin(7k) is sin(7k) 1/3 e^{3x}+C