1) ∫(7x^(3) - 4x^(2) +9x -10)dx

2) ∫ [(6 √(x)+2)/ √(x)]

3) ∫6x^(7) +4 / (x)

Thanks

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- Dec 11th 2008, 05:39 PMbgwarhawkIndefinite integral
1) ∫(7x^(3) - 4x^(2) +9x -10)dx

2) ∫ [(6 √(x)+2)/ √(x)]

3) ∫6x^(7) +4 / (x)

Thanks - Dec 11th 2008, 06:01 PMSkalkaz
Dear bgwarhawk,

these are elementary intagrals. You must recall the formula:

$\displaystyle \int x^a dx = x^{a+1}/a+C$ (if a <> -1) - Dec 11th 2008, 06:09 PMbgwarhawk
- Dec 11th 2008, 06:20 PMSkalkaz
This is a formula from second page in a book about integral. What is your problem? Where did you get stuck? Or do you think this forum is a automatic solution generator of homework?

- Dec 11th 2008, 06:26 PMbgwarhawk
- Dec 11th 2008, 07:00 PMSkalkaz
the 1st term is incorrect. And don't forget the C at the end.

- Dec 11th 2008, 07:44 PMErdos32212
- Dec 11th 2008, 07:48 PMProve It
- Dec 11th 2008, 07:49 PMProve It
- Dec 11th 2008, 07:51 PMProve It
- Dec 12th 2008, 08:06 AMbgwarhawk
- Dec 13th 2008, 01:44 AMProve It
Use the formula $\displaystyle \int x^a dx = \frac{1}{a + 1}x^{a+1}+C$.

$\displaystyle \int{6 + 2x^{-\frac{1}{2}}\,dx} = \int{6x^0 + 2x^{-\frac{1}{2}}\,dx}$

$\displaystyle = \frac{6}{1}x^1 + \frac{2}{\frac{1}{2}}x^{\frac{1}{2}} + C$

$\displaystyle = 6x + 4x^{\frac{1}{2}} + C$

$\displaystyle = 6x + 4\sqrt{x} +C$.