Indefinite Integral: int(the fifth root of x^2 - 1 / x^3) dx

[cmnalo]

∫(the fifth root of x^2 - 1 / x^3)dx

∫x^5/2 dx - ∫ 1 / x^3 dx

[(1 / 5/2 +1 )(x^5/2 +1)] - [(1 / -1/3 +1)(x^-1/3 +1)] +c

2/7x^7/2 - 3/2x^2/3 + c

where did I go wrong?

Answer:

(5/7)x^7/5+1/2x^2+C

 

[stapel]

∫(the fifth root of x^2 - 1 / x^3)dx

Would it be correct to rewrite the integral as follows?

. . . . .\(\displaystyle \L \int\, \left(x^{\frac{2}{5}}\, -\, x^{-3}\right)\, dx\)

Thank you.

Eliz.

 

[cmnalo]

∫x^5/2 dx - ∫ x^-3 dx

1 / (5/2 + 1) x^5/2+1 - 1 / (-3 + 1) x^-3 + 1 + c

2/7x^7/2 - 1/-2x^-2 + c

Still not working out for me. Any suggestions.

 

[stapel]

If the integral can be rewritten in the manner asked about earlier, then I don't believe the book's answer is correct. But if your initial posting was misunderstood, then the book's answer may be right. It would be helpful if you could respond to the earlier question.

Thank you.

Eliz.

 

[cmnalo]

Yes I do believe your rewrite of the integral is correct.

 

[skeeter]

antiderivative of x^2/5 is (5/7)x^7/5

antiderivative of -x^-3 is (1/2)x^-2

put 'em together ...

(5/7)x^7/5 + (1/2)x² + C