Question

Help Please!
Evaluate the following integral. (below)

Answer 1

\[\int\limits_{}^{} \frac{x^ \frac{ 7 }{ 2 } + x^\frac{ 3 }{ 2 } }{ x } dx\]

Answer 2

@zepdrix

Answer 3

We can rewrite this as 2 separate fractions.
\[\large\int\limits\limits\frac{x^{7/2}+x^{3/2}}{x} dx \qquad=\qquad \int\limits\frac{x^{7/2}}{x}+\frac{x^{3/2}}{x}dx\]

Answer 4

From here we'll apply rules of exponents.\[\large \int\limits\limits\frac{x^{7/2}}{x^1}+\frac{x^{3/2}}{x^1}dx \qquad=\qquad\int\limits x^{7/2-1}+x^{3/2-1}dx\]When we divide terms of similar bases (x in this case), we `subtract` the exponents.

Answer 5

so kind of like reversing a fraction?

Answer 6

Ya :)

Answer 7

Make sure you do your subtraction correctly, we get something like this,\[\large \int\limits x^{5/2}+x^{1/2}dx\]

Answer 8

The integration might be a little tricky, since we'll be dividing by a fraction.
Here is what the first term would give us,\[\large \frac{x^{5/2+1}}{5/2+1} \qquad=\qquad \frac{x^{7/2}}{(7/2)} \qquad=\qquad \frac{2}{7}x^{7/2}\]

Answer 9

then from there, product rule??

Answer 10

product rule? :o
no, just power rule.

Answer 11

and the 2nd term would be 3/2x^3/2?

Answer 12

it would be x^3/2 divided by 3/2.
Since we're dividing by a fraction it would flip, giving us,

(2/3)x^3/2

Answer 13

oh okay. so it would be
\[\frac{ 2 }{ 7 }x ^\frac{ 7 }{ 2 } + \frac{ 2 }{ 3 }x^\frac{ 3 }{ 2 }\]

Answer 14

\[+C\]

Answer 15

yay good job \c:/

Answer 16

Thank you so muchhhhh!!! (:

Answer 17

for all your help