anonymous
  • anonymous
integrate x^33^x dx
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
product of x raised to power three and 3 raised to power x
anonymous
  • anonymous
i assume this is \[\int x^33^xdx\]
anonymous
  • anonymous
ya

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anonymous
  • anonymous
it is a set up for integration by parts, but you have to do it 3 times ! will reduce the power on \[x^3\] once each time
anonymous
  • anonymous
i have assumed f(x)=x^3 and g'(x)=3^x
anonymous
  • anonymous
for example in the first time you will put \[u=x^3, dv=3^xdx, du=3x^2,v=\frac{3^x}{\ln(3)}\] and get \[uv-\int vdu=\frac{x^33^x}{\ln(3)}-\frac{3}{\ln(3)}\int x^23^xdx\]
anonymous
  • anonymous
then lather, rinse, repeat. hold on
anonymous
  • anonymous
easier to read it , click "show steps" http://www.wolframalpha.com/input/?i=x^3*3^x+dx
anonymous
  • anonymous
how would u integrate 3x^2.3^x/log3
anonymous
  • anonymous
first of all pull out the constants like i did above and get \[-\frac{3}{\ln(3)}\int x^23^xdx\] then repeat the parts, this time with \[u=x^2\]
anonymous
  • anonymous
ur ans went over my head
anonymous
  • anonymous
ok it is confusing, but if you got the first one right you should have a good idea what is going on each time you integrate by parts, you will reduce the power by one when you take the derivative of \[x^3, x^2, x\]
anonymous
  • anonymous
don't forget that \[\ln(3)\] is a number (constant) so it come right out front of the integral sign
anonymous
  • anonymous
your next job is really \[\int x^2 3^xdx\] the constant just sits out front. integrate by parts again
anonymous
  • anonymous
let me show u the first step......3x^2.3x/log3-integrate3x^2.3^x/log3 dx
anonymous
  • anonymous
ah first step is wrong that is the problem
anonymous
  • anonymous
it is \[\int udv=uv-\int vdu\]
anonymous
  • anonymous
i dnt use that formula
anonymous
  • anonymous
\[u=x^3,du = 3x^2, dv = 3^x, v = \int 3^x=\frac{3^x}{\ln(3)}\]
anonymous
  • anonymous
\[uv=\frac{x^33^x}{\ln(3)}\]
anonymous
  • anonymous
and i stress again, even though the second one is \[-\int \frac{3x^23^x}{\ln(3)}dx\] you should rewrite it immediately as \[-\frac{3}{\ln(3)}\int x^23^xdx\]
anonymous
  • anonymous
i m having trouble with the formula implementation......wht to do?

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