KatClaire
Find the integral!!!



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KatClaire
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\[\int\limits_{}^{} \frac{ 3 }{ \sqrt[3]{3x5} } dx\]

KatClaire
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I really don't have much a clue for this one

Yahoo!
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Let
3x  5 = u

Yahoo!
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Now..Use Substitution Method

KatClaire
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and I take out the 3 on top right?

Mimi_x3
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\(u=3x+5\)
du/dx=3
\[\int\limits\frac{3}{\sqrt[3]{u}} *\frac{du}{3} =>\int\limits\frac{1}{\sqrt[3]{u}} du=>\int\limits\frac{1}{u^{1/3}} du\]

Yahoo!
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du / dx = 3
du = 3 dx

Mimi_x3
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u=3x5**

KatClaire
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perfect! I'll try it again

KatClaire
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would it be
\[\frac{ 3(3x5)^{2/3} }{ 2 } +c\]

Ravi2
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is this method called integration by substitution method??

KatClaire
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I think so

sirm3d
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you can also try \[y=\sqrt[3]{3x5}\Rightarrow y^3=3x5\\3y^2\;\mathrm dy =3\;\mathrm dx\]

Ravi2
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yup.....also an other way is by doing direct inverse power......