Question

Find the integral!!!

Answer 1

\[\int\limits_{}^{} \frac{ 3 }{ \sqrt[3]{3x-5} } dx\]

Answer 2

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

Answer 3

Let

3x - 5 = u

Answer 4

Now..Use Substitution Method

Answer 5

and I take out the 3 on top right?

Answer 6

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

Answer 7

du / dx = 3

du = 3 dx

Answer 8

u=3x-5**

Answer 9

perfect! I'll try it again

Answer 10

would it be
\[\frac{ 3(3x-5)^{2/3} }{ 2 } +c\]

Answer 11

is this method called integration by substitution method??

Answer 12

I think so

Answer 13

you can also try \[y=\sqrt[3]{3x-5}\Rightarrow y^3=3x-5\\3y^2\;\mathrm dy =3\;\mathrm dx\]

Answer 14

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