Question

Can somebody please help me evaluate this indefinite integral?
(x^4 -x^3)/sqrt(x)

Answer 1

Split the fraction.

Answer 2

probably easiest just to simplify the integral by dividing each term individually by the x^(-1/2)

Answer 3

err, multiply if it's a negative exponent.

Answer 4

ok, let me try that, i'll just integrate each term individually over the sqrt(x).

Answer 5

Good.

Answer 6

ok, the fractional exponents tripped me up a bit, but this is what I came up with:
[8x^(9/2) - 10x^(7/2)]/20
I can show you my steps, if you'd like. Can you guys tell me if this is correct?

Answer 7

Not quite what I get. I get different coefficients.

Answer 8

Same here. The exponents are right.

Answer 9

hmm, well what did you get for coefficients?
I had 2x^(9/2)/5 - 2x^(7/2)/4 and I multiplied to get 20 as a common denominator, but I think that's right.
Let me check my work over...

Answer 10

Remember, add one to the exponent, THEN divide by it, for the power rule.

Answer 11

i'm still confused, if the exponents are -1/2 so +1 would be 1/2 and divided by 1/2 would be 2x^(1/2)/1 right?

Answer 12

\[\frac{x^4 - x^3}{x^{1/2}} = \frac{x^4}{x^{1/2}}-\frac{x^3}{x^{1/2}} = x^{\frac{7}{2}} - x^{\frac{5}{2}}\]

Answer 13

That looks strange to me, but the exponents before integration should be 7/2 and 5/2 (4- 1/2, and 3 - 1/2)

Answer 14

ok so after integration it would be 2x^(9/2)/9 - 2x^(7/2)/7 ?

Answer 15

14x^(9/2) - 18x^(7/2)/63 ?

Answer 16

Looks good. I normally leave the coefficients as individual fractions, but your teacher may not want that.

Answer 17

ok thank you so much for your help! I understand this much more than when we started, so yay!

Answer 18

Outstanding :)

Keep at 'em. They get easier to do :)