anonymous
  • anonymous
Find the integral!!!
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[\int\limits_{}^{} \frac{ 3 }{ \sqrt[3]{3x-5} } dx\]
anonymous
  • anonymous
I really don't have much a clue for this one
anonymous
  • anonymous
Let 3x - 5 = u

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anonymous
  • anonymous
Now..Use Substitution Method
anonymous
  • anonymous
and I take out the 3 on top right?
Mimi_x3
  • Mimi_x3
\(u=3x+5\) du/dx=3 \[\int\limits\frac{3}{\sqrt[3]{u}} *\frac{du}{3} =>\int\limits\frac{1}{\sqrt[3]{u}} du=>\int\limits\frac{1}{u^{1/3}} du\]
anonymous
  • anonymous
du / dx = 3 du = 3 dx
Mimi_x3
  • Mimi_x3
u=3x-5**
anonymous
  • anonymous
perfect! I'll try it again
anonymous
  • anonymous
would it be \[\frac{ 3(3x-5)^{2/3} }{ 2 } +c\]
anonymous
  • anonymous
is this method called integration by substitution method??
anonymous
  • anonymous
I think so
sirm3d
  • sirm3d
you can also try \[y=\sqrt[3]{3x-5}\Rightarrow y^3=3x-5\\3y^2\;\mathrm dy =3\;\mathrm dx\]
anonymous
  • anonymous
yup.....also an other way is by doing direct inverse power......

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