Integration

Gobles

By any chance would any of you know how to integrate

(7x^2-13x+13)/((x-2)(x^2-2x+3))

Its a question on my homework and I think I’m supposed to integrate by partial fractions, but I can’t seem to get it to work.

element

errolzzz

@gobles Bruh what

terrible2koldman

@gobles

The first term is, x2 its coefficient is 1 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is +3

Step-1 : Multiply the coefficient of the first term by the constant 1 • 3 = 3

Step-2 : Find two factors of 3 whose sum equals the coefficient of the middle term, which is -2 .

 	-3	   +   	-1	   =   	-4	
 	-1	   +   	-3	   =   	-4	
 	1	   +   	3	   =   	4	
 	3	   +   	1	   =   	4

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Equation at the end of step
1
:

STEP
2
:

Equation at the end of step
2
:

STEP
3
:

             7x2 - 13x + 13

Simplify ———————————————————————
(x - 2) • (x2 - 2x + 3)
Trying to factor by splitting the middle term

3.1 Factoring 7x2 - 13x + 13

The first term is, 7x2 its coefficient is 7 .
The middle term is, -13x its coefficient is -13 .
The last term, "the constant", is +13

Step-1 : Multiply the coefficient of the first term by the constant 7 • 13 = 91

Step-2 : Find two factors of 91 whose sum equals the coefficient of the middle term, which is -13 .

 	-91	   +   	-1	   =   	-92	
 	-13	   +   	-7	   =   	-20	
 	-7	   +   	-13	   =   	-20	
 	-1	   +   	-91	   =   	-92	
 	1	   +   	91	   =   	92	
 	7	   +   	13	   =   	20	
 	13	   +   	7	   =   	20	
 	91	   +   	1	   =   	92

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :
7x2 - 13x + 13
———————————————————————
(x - 2) • (x2 - 2x + 3)

Just messing. Got this from Google. No idea what your question actually means.

Petravork

@terrible2koldman said in Integration:

@gobles

The first term is, x2 its coefficient is 1 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is +3

Step-1 : Multiply the coefficient of the first term by the constant 1 • 3 = 3

Step-2 : Find two factors of 3 whose sum equals the coefficient of the middle term, which is -2 .
 	-3	   +   	-1	   =   	-4	
 	-1	   +   	-3	   =   	-4	
 	1	   +   	3	   =   	4	
 	3	   +   	1	   =   	4	
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Equation at the end of step
1
:

STEP
2
:

Equation at the end of step
2
:

STEP
3
:
             7x2 - 13x + 13    
Simplify ———————————————————————
(x - 2) • (x2 - 2x + 3)
Trying to factor by splitting the middle term

3.1 Factoring 7x2 - 13x + 13

The first term is, 7x2 its coefficient is 7 .
The middle term is, -13x its coefficient is -13 .
The last term, "the constant", is +13

Step-1 : Multiply the coefficient of the first term by the constant 7 • 13 = 91

Step-2 : Find two factors of 91 whose sum equals the coefficient of the middle term, which is -13 .
 	-91	   +   	-1	   =   	-92	
 	-13	   +   	-7	   =   	-20	
 	-7	   +   	-13	   =   	-20	
 	-1	   +   	-91	   =   	-92	
 	1	   +   	91	   =   	92	
 	7	   +   	13	   =   	20	
 	13	   +   	7	   =   	20	
 	91	   +   	1	   =   	92	
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :
7x2 - 13x + 13
———————————————————————
(x - 2) • (x2 - 2x + 3)

Just messing. Got this from Google. No idea what your question actually means.