# Thread: Indefinite Integral Problem- Can anyone check my work

1. ## Indefinite Integral Problem- Can anyone check my work

$\displaystyle \int (\frac{2}{3x^4})dx$
$\displaystyle \int (2\times{3x^{-4}})dx$
$\displaystyle \int (6x^{-4})dx$
$\displaystyle 6\int (x^{-4})dx$
$\displaystyle 6 (\frac{x^{-3}}{-3})+c$

$\displaystyle -2x^{-3}+c$

$\displaystyle \frac{-2}{x^3}+c$

Thanks!

2. Originally Posted by Jim Marnell
$\displaystyle \int (\frac{2}{3x^4})dx$

$\displaystyle \int{ (2\times {\color{red}3} x^{-4}})dx$

The three in first step was in denominator
the second step should be

$\displaystyle \frac{1}{3}\int (2\times{x^{-4}})dx$

Thanks!
Red

3. $\displaystyle \int (\frac{2}{3x^4})dx$

$\displaystyle \frac{1}{3}\int (2\times{x^{-4}})dx$

$\displaystyle \frac{1}{3}\int (2x^{-4})dx$

$\displaystyle \frac{1}{3}\times{2}\int (x^{-4})dx$

$\displaystyle \frac{2}{3}\times{\frac{x^{-3}}{-3}}+c$

$\displaystyle \frac{-2}{9}x^{-3}+c$

$\displaystyle \frac{\frac{2}{9}}{x^3}+c$

I'm not sure if my final step is right. Thanks for any help!

4. Originally Posted by Jim Marnell
$\displaystyle \int (\frac{2}{3x^4})dx$

$\displaystyle \frac{1}{3}\int (2\times{x^{-4}})dx$

$\displaystyle \frac{1}{3}\int (2x^{-4})dx$

$\displaystyle \frac{1}{3}\times{2}\int (x^{-4})dx$

$\displaystyle \frac{2}{3}\times{\frac{x^{-3}}{-3}}+c$

$\displaystyle \frac{-2}{9}x^{-3}+c$

$\displaystyle \frac{\frac{{\color{red}-}2}{9}}{x^3}+c$

You forgot "-" sign , his can further be written as

$\displaystyle \frac{-2}{9x^3}+c$

I'm not sure if my final step is right. Thanks for any help!
Red

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