Question

Evaluate: int(dx/x^{2}-4x+5)

Answer 1

I mean:\[\int\limits(dx/x^{2}-4x+5)\]

Answer 2

you can also write this like \[\int\limits (1/x^2-4x+5)dx\]

Answer 3

\[\int\limits(\frac{ 1 }{ x^2 }-4x+5)dx=-\frac{ 1 }{ x }-2x^2+5x\]

Answer 4

sorry + C
cant forget the constant 'C' since this is an indefinite integral

Answer 5

please clear step 2: (-1/x-2x^2+5x)

Answer 6

did this help @bittuaryan ?

Answer 7

@sjerman1 How (1/(x^2−4x+5)) is change to ((1/x^2)−4x+5).

Answer 8

haha
well you need to specify with parentheses because i thought only the first term was 1/x^2 ...

Answer 9

well then in this case since x^2-4x+5 can not be factored we can complete the square to get something that can be used

Answer 10

atan(-2+x) is the answer

Answer 11

after completing the square we get 1/(x-2)^2+1

Answer 12

use u-sub for x-2 and get 1/(u^2+1)

Answer 13

\[x ^{2}-4x+5=(x-5)(x+1)\]

Answer 14

sjerman1 is correct

Answer 15

we know that 1/u^2+1 is arctan so arctan(u)

Answer 16

then just plug in u=x-2

Answer 17

atan(x-2)

Answer 18

I verified in matlab. good job.

Answer 19

and @fmg78360 has the answer -> arctan(x-2)

Answer 20

I cheated you did the actual work

Answer 21

we all did good here. and now we know how to do it!

Answer 22

did you mean: \[\int\limits \frac{ dx }{ x^2-4x+5 }\]

Answer 23

yes, @abb0t he did, but i didn't catch that in the beginning.

Answer 24

Use partial fraction decomposition to solve the integral:
\[\int\limits\limits \frac{ 1 }{ x^2-4x+5 }dx \neq \int\limits\limits \frac{ 1 }{ (x-5)(x+1) }\]

Answer 25

or you can use completing the square like i did

Answer 26

The integral was solved using the arctan integral identity.

Answer 27

I didn't see. But complete the square works.