Recent content by ComFlu945

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    Nonhomogeneous Boundary Value Problem

    I'm working on the exact same problem, any update?
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    Undergrad What's a general way to integrate f(x)*exp(n*x)

    title says it all
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    How would I integrate exp(x)*cos(x)

    Homework Statement How would I integrate exp(x)*cos(x), exp is referring to euler's number Homework Equations The Attempt at a Solution u substitution doesn't work
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    High School When a stream hits a surface, why does the stream always split in two?

    If if the stream hits the surface at a sharp angle, it splits in two directions. Why is that?
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    Graduate Help figuring out this trigometric substitution

    I figured it out. Let O=N+iM. Then let O=R*e^-i*theta
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    Undergrad How to Simplify This Equation with x=z+1?

    I'm trying to follow some notes in class. so the original equation is: u= [ (x^2 – 1)^1/2 + ln (x + (x^2 – 1)^1/2 )] and we let x=z+1. Then by simplifying and approximating, u=z*2*2^.5 + higher order terms from my notes: (x^2 – 1)^1/2 = (2z)^.5*(1+z/2)^.5 ln(1+e) approximately = e
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    Graduate Help figuring out this trigometric substitution

    From my notes I have w=u(x+iy)*(x^2 - y^2 +k^2 + i(2xy))^-.5 We let N=x^2-y^2+k^2 M=2xy R^2=(N^2+M^2)^2 theta=tan^-1(M/N) using this, now w=u(x+iy)*(cos(theta/2)-isin(theta/2))*(x^2 - y^2 +k^2 )^2 + (2xy)^2 )^-.25 I don't get that part. Btw, it simplifies to...
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    Undergrad How do I integrate this? x/(x^2-1)^.5

    Thanks! First one worked like a charm. For second one I substituted x for cosh(y). Since cosh(y)^2-1=sinh(y)^2, but bottom turns into sinh(y). And since x=cosh(y), dx/dy= sinh(y). Back to original equation: integral( 1/(x^2-1)^.5 dx) = integral ( sinh(y)/sinh(y)) dy = 1 + constant...
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    Undergrad How do I integrate this? x/(x^2-1)^.5

    How do I integrate this? 1/(x^2-1)^.5 How do I integrate this? x/(x^2-1)^.5 And this 1/(x^2-1)^.5