Question

integral of 1/x * (2/3)x^(3/2)

Answer 1

Is it:
\[\large \int\limits\frac{1}{x} *\frac{2}{3} x^{\frac{3}{2}} \] ?

Answer 2

yes

Answer 3

\[\frac1x\cdot\frac23x^{3/2}=\frac23x^{1/2}\]

Answer 4

and how exactly did you get that answer? sorry i just needa know for future reference

Answer 5

\[\large \int\limits\frac{2}{3} \sqrt{x} =>\int\limits\frac{2\sqrt{x}}{3} =>\frac{2}{3} \int\limits\sqrt{x} \]
The integrate it

Answer 6

Then*

Answer 7

...with the rule\[\large \int x^ndx=\frac{x^{n+1}}{n+1}+C\]

Answer 8

ok but i still have a question if you dont mind answering...how did you get from 1/x*(2/3)x^(2/3) to 2/3(x^1/2)??

Answer 9

like do you just take the intergral of them both seperately or what? im so confused

Answer 10

algebra\[\large\frac{x^a}{x^b}=x^{a-b}\]\[\frac1x\cdot\frac23x^{3/2}=\frac23\frac {x^{3/2}}x=\frac23x^{3/2-1}=\frac23x^{1/2}\]now integrate\[\frac23\int x^{1/2}dx=\frac23\frac{x^{\frac12+1}}{\frac12+1}=x^{3/2}+C\]

Answer 11

ohhhhh ok i see now i see! yayy thank you

Answer 12

welcome :D