Proving Integrals: e^(au)sin(bu), e^(au)cos(bu), sec^3u du

[nameVoid]

looking for proofs of the following integrals

integral ( e^(au)sin(bu)du ) and integral(e^(au)cos(bu)du) and integral (sec^3u du)

 

[Mark44]

The first two can be done by integrating by parts twice. After the second integration, you end up with the integral you started with, and you can solve algebraically for the integral. In both problems, start with u = e^(au) and dv = sin(bu)du or cos(bu)du. After integrating the first time, do it again, with u = e^(au) again, and dv being whatever is left.

The third one can also be done by integration by parts, I believe. Try u = sec u and dv = sec^2(u) du.

 

[Physics_Math]

also remember your trig derivatives:

d/dx(secx)=tanxsecx and
d/dx(tanx)=sec²x

 

[Count Iblis]

$$\int \exp(p x) dx = \frac{1}{p}\exp(px) + c$$

Take p = a + b i and equate the real and imaginary parts of both sides. You should be able do this mentally in your head (multiplying the numerator and denominator by the complex conjugate of p isn't that difficult).

 

[nameVoid]

im looking for somthing along the lines of integration by parts a link to proofs would be nice

 

[Mark44]

im looking for somthing along the lines of integration by parts a link to proofs would be nice

Your problem isn't a proof. All you need to do is carry out the integration, and I have given you a start on how to do that.

 

[Physics_Math]

Do you mean that you want a proof of the actual method of integration by parts? If so, then consider the product rule of differentiation:

d/dx(f*g)=f'*g + f*g'

Now integrate both sides of the equation and you get you proof.

Is that what you were looking for?