Se^(3x)cos(2x)dx S=Integral

Tutors, sign in to answer this question.

Marked as Best Answer

The first step is to convert the cosine function to the exponential form using Euler's formula.

Cos(2x) = 1/2 * [e^(i2x)-e^(-i2x)]

The next step is to distribute the outside exponential that is 1/2*[e^(3x+i2x)-e^(3x-i2x)].

Now the integral becomes a very simple u and v substitution integral. That is let u = (3+i2)x and v = (3-i2)x therefore du = (3+i2)dx and dv = (3-i2)dx.

Is this far enough help or do you need the next steps?

You can do it by applying the integration by parts.

∫e^{3x}cos(2x)dx=(½)e^{3x}sin(2x)-(3/2)∫e^{3x}sin(2x)dx=(½)e^{3x}sin(2x)-(¾)e^{3x}(-cos(2x))-(9/4)∫e^{3x}cos(2x)dx

Now let I=∫e^{3x}cos(2x)dx; Then we have an equation:

I=(½)e^{3x}sin(2x)+(¾)e^{3x}cos(2x)-(9/4)I;

Solving for I yields:

I=1/13*[2e^{3x}sin(2x)+3e^{3x}cos(2x)]=e^{3x}/13*[2sin(2x)+3cos(2x)]

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Mark D.

Experienced Tutor Specializing in Mathematics and Chemistry

$11.25 per 15 min

View Profile >

Deepa K.

Effective Math Tutor for academic and Test Prep Skills

$15 per 15 min

View Profile >

Tomas G.

Experienced Tutor for more than 10 years

$7.50 per 15 min

View Profile >

## Comments