Question

Integrate(2x^-5).
How do you do this question?

Answer 1

is it \(\large\color{black}{\displaystyle\int\limits_{~}^{~}2x^{-5}dx}\) ?

Answer 2

yes

Answer 3

then you can take the constant out,
like this: 2\(\large\color{black}{\displaystyle\int\limits_{~}^{~}x^{-5}dx}\)

and apply the power rule.

Answer 4

\(\large\color{black}{2\displaystyle\int\limits_{~}^{~}x^{-5}dx=2\times \frac{\LARGE x^{-5\color{red}{+1}} }{\LARGE \color{red}{-5+1}}+C}\)

Answer 5

what do you get as your answer?

Answer 6

(2(x^-4)/(-4))

Answer 7

yes, right: \(\large\color{black}{ 2 \times \frac{\LARGE x^{-4} }{\LARGE -4} +C }\) but you can simplify this a bit more

Answer 8

-(x^-4/2)

Answer 9

yup, \(\large\color{black}{ \frac{\LARGE x^{-4} }{\LARGE -2} +C }\)

Answer 10

thank you..

Answer 11

or, \(\large\color{black}{ -\frac{\LARGE x^{-4} }{\LARGE 2} +C }\) same thing

Answer 12

what does your teacher require to to farther do, does (s)he want you to re-write using a positive exponent?

Answer 13

or would this result satisfy your teacher?

Answer 14

Yes this result works

Answer 15

okay, but make sure to include the +C :)

Answer 16

You\(\normalsize\color{blue}{ \rm ~welcome! }\)