Use a table of integrals with forms involving eu to find the indefinite integral ∫e−4xsin⁡3xdx

Joseph Krupa

Joseph Krupa

Answered

2021-12-29

Use a table of integrals with forms involving eu to find the indefinite integral e4xsin3xdx

Answer & Explanation

braodagxj

braodagxj

Expert

2021-12-30Added 38 answers

Step 1
By using the table of integrals we are to find the indefinite integral:
e4xsin3xdx
Step 2
We will use formula from the table of integrals with forms involving eu:
euxsinvxdx=euxu2+v2[usinvxvcosvx]+C...(1)
We are to find the indefinite integral e4xsin3xdx
So, Here u=-4 and v=3
On Putting u=-4 and v=3 in (1) we get:
e4xsin3xdx=e4x(4)2+(3)2[4sin3x3cos3x]+C
e4xsin3xdx=e4x25[4sin3x3cos3x]+C
or e4xsin3xdx=e4x25[4sin3x+3cos3x]+C
lenkiklisg7

lenkiklisg7

Expert

2021-12-31Added 29 answers

e4xsin(3x)dx
The formula for integration by parts:
U(x)dV(x)=U(x)V(x)V(x)dU(x)
We put
U=1
dV=dx
Then:
dU=0dx
V=x
Therefore:
e4xsin(3x)dx=x
Answer:
e4xsin(3x)=x+C
Vasquez

Vasquez

Expert

2022-01-07Added 457 answers

e4xsin(3x)dx=e4xsin(3x)43e4xcos(3x)4dx=e4xsin(3x)4(3e4xcos(3x)169e4xsin(3x)16dx)=e4xsin(3x)4(3e4xcos(3x)16+916e4xsin(3x)dx)=4e4xsin(3x)3e4xcos(3x)25e4xsin(3x)dx=4e4xsin(3x)3e4xcos(3x)25+C=e4x(4sin(3x)+3cos(3x))25+C

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