Joseph Krupa

Answered

2021-12-29

Use a table of integrals with forms involving eu to find the indefinite integral $\int {e}^{-4x}\mathrm{sin}3xdx$

Answer & Explanation

braodagxj

Expert

2021-12-30Added 38 answers

Step 1

By using the table of integrals we are to find the indefinite integral:

$\int {e}^{-4x}\mathrm{sin}3xdx$

Step 2

We will use formula from the table of integrals with forms involving$e}^{u$ :

$\int {e}^{ux}\mathrm{sin}vxdx=\frac{{e}^{ux}}{{u}^{2}+{v}^{2}}[u\mathrm{sin}vx-v\mathrm{cos}vx]+C$ ...(1)

We are to find the indefinite integral$\int {e}^{-4x}\mathrm{sin}3xdx$

So, Here u=-4 and v=3

On Putting u=-4 and v=3 in (1) we get:

$\int {e}^{-4x}\mathrm{sin}3xdx=\frac{{e}^{-4x}}{{(-4)}^{2}+{\left(3\right)}^{2}}[-4\mathrm{sin}3x-3\mathrm{cos}3x]+C$

$\int {e}^{-4x}\mathrm{sin}3xdx=\frac{{e}^{-4x}}{25}[-4\mathrm{sin}3x-3\mathrm{cos}3x]+C$

or$\int {e}^{-4x}\mathrm{sin}3xdx=-\frac{{e}^{-4x}}{25}[4\mathrm{sin}3x+3\mathrm{cos}3x]+C$

By using the table of integrals we are to find the indefinite integral:

Step 2

We will use formula from the table of integrals with forms involving

We are to find the indefinite integral

So, Here u=-4 and v=3

On Putting u=-4 and v=3 in (1) we get:

or

lenkiklisg7

Expert

2021-12-31Added 29 answers

The formula for integration by parts:

We put

U=1

dV=dx

Then:

dU=0dx

V=x

Therefore:

Answer:

Vasquez

Expert

2022-01-07Added 457 answers

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