Question

HELP!!! I will give medal to anyone who can explain how they got their answer. Evaluate if it exists:

Answer 1

\[\int\limits_{0}^{\ln(2)}x ^{-2}e ^{-1/x}dx\]

Answer 2

u sub. let u = 1/x then du = -1/x^2=-x^-2

Answer 3

Thanks again can you answer one more question?

Answer 4

\[\int\limits_{?}^{?}\frac{ 1 }{ \sqrt{7+6x-x ^{2}} }\]There is no bounds just integral

Answer 5

is that everything?

Answer 6

Yes no bounds just integral

Answer 7

\[\int\frac{dx}{7+6x-x^{2}}\] like this?

Answer 8

Yes

Answer 9

No the denominator is square-rooted

Answer 10

oops... I meant
\[\int\frac{dx}{\sqrt{7+6x-x^{2}}}\]
like this?

Answer 11

Yea

Answer 12

you need to complete the square of the polynomial inside the square root, i.e., complete the square on 7+6x_x^2.
then you it should be an inverse trig. function (once integrated).

Answer 13

When you mean complete the square, do you mean factor?

Answer 14

no, i mean complete the square. look at this website
http://www.math.hmc.edu/calculus/tutorials/complete_sq/

Answer 15

I got x^2+6x+9=2 is that right?

Answer 16

it should be 16-(x-3)^2 = 16 - x^2 +6x -9 = 7+6x-x^2

Answer 17

Oh ok so is the trig identity the sine inverse one?

Answer 18

I think so... it's been a while

Answer 19

Thanks for the help.