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How to use it?
- Integral of d{x}:
-
Integral of xcosx²
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Integral of (x^2-3x)×sin(2x)
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Integral of sin^5x/cos^4x
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Integral of 6x⁵
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Identical expressions
- one /(two x^2-12x+ twenty-six)
- 1 divide by (2x squared minus 12x plus 26)
- one divide by (two x squared minus 12x plus twenty minus six)
- 1/(2x2-12x+26)
- 1/2x2-12x+26
- 1/(2x²-12x+26)
- 1/(2x to the power of 2-12x+26)
- 1/2x^2-12x+26
- 1 divide by (2x^2-12x+26)
- 1/(2x^2-12x+26)dx
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Similar expressions
- 1/(2x^2+12x+26)
- 1/(2x^2-12x-26)
Integral of 1/(2x^2-12x+26) dx
The solution
You have entered
[src]
1 / | | 1 | 1*---------------- dx | 2 | 2*x - 12*x + 26 | / 0
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{2 x^{2} - 12 x + 26}\, dx$$
Integral(1/(2*x^2 - 12*x + 26), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | 1*1*---------------- dx | 2 | 2*x - 12*x + 26 | /
Rewrite the integrand
1 1
1*---------------- = ------------------
2 / 2 \
2*x - 12*x + 26 |/ x 3\ |
8*||- - + -| + 1|
\\ 2 2/ /or
/ | | 1 | 1*1*---------------- dx | 2 = | 2*x - 12*x + 26 | /
/
|
| 1
| -------------- dx
| 2
| / x 3\
| |- - + -| + 1
| \ 2 2/
|
/
--------------------
8 In the integral
/
|
| 1
| -------------- dx
| 2
| / x 3\
| |- - + -| + 1
| \ 2 2/
|
/
--------------------
8 do replacement
3 x
v = - - -
2 2then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
8 8 do backward replacement
/
|
| 1
| -------------- dx
| 2
| / x 3\
| |- - + -| + 1
| \ 2 2/ / 3 x\
| atan|- - + -|
/ \ 2 2/
-------------------- = -------------
8 4 Solution is:
/ 3 x\
atan|- - + -|
\ 2 2/
C + -------------
4
The answer (Indefinite)
[src]
/ / 3 x\ | atan|- - + -| | 1 \ 2 2/ | 1*---------------- dx = C + ------------- | 2 4 | 2*x - 12*x + 26 | /
$${{\arctan \left({{2\,x-6}\over{4}}\right)}\over{4}}$$
The graph
The answer
[src]
pi atan(3/2) - -- + --------- 16 4
$${{\arctan \left({{3}\over{2}}\right)}\over{4}}-{{\pi}\over{16}}$$
=
=
pi atan(3/2) - -- + --------- 16 4
$$- \frac{\pi}{16} + \frac{\operatorname{atan}{\left(\frac{3}{2} \right)}}{4}$$
The graph
Use the examples entering the upper and lower limits of integration.