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How to use it?
- Integral of d{x}:
-
Integral of 45x
-
Integral of 1/(x^6+x^4)
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Integral of sin^3xcos^2xdx
- Integral of 4t-t^2
-
Identical expressions
- dx/(x^ two +12x+ forty-five)
- dx divide by (x squared plus 12x plus 45)
- dx divide by (x to the power of two plus 12x plus forty minus five)
- dx/(x2+12x+45)
- dx/x2+12x+45
- dx/(x²+12x+45)
- dx/(x to the power of 2+12x+45)
- dx/x^2+12x+45
- dx divide by (x^2+12x+45)
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Similar expressions
- dx/(x^2-12x+45)
- dx/(x^2+12x-45)
Integral of dx/(x^2+12x+45) dx
The solution
You have entered
[src]
1 / | | 1 | 1*-------------- dx | 2 | x + 12*x + 45 | / 0
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{x^{2} + 12 x + 45}\, dx$$
Integral(1/(x^2 + 12*x + 45), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | 1*1*-------------- dx | 2 | x + 12*x + 45 | /
Rewrite the integrand
1 1
1*-------------- = ------------------
2 / 2 \
x + 12*x + 45 |/ x \ |
9*||- - - 2| + 1|
\\ 3 / /or
/ | | 1 | 1*1*-------------- dx | 2 = | x + 12*x + 45 | /
/
|
| 1
| -------------- dx
| 2
| / x \
| |- - - 2| + 1
| \ 3 /
|
/
--------------------
9 In the integral
/
|
| 1
| -------------- dx
| 2
| / x \
| |- - - 2| + 1
| \ 3 /
|
/
--------------------
9 do replacement
x
v = -2 - -
3then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
9 9 do backward replacement
/
|
| 1
| -------------- dx
| 2
| / x \
| |- - - 2| + 1
| \ 3 / / x\
| atan|2 + -|
/ \ 3/
-------------------- = -----------
9 3 Solution is:
/ x\
atan|2 + -|
\ 3/
C + -----------
3
The answer (Indefinite)
[src]
/ / x\ | atan|2 + -| | 1 \ 3/ | 1*-------------- dx = C + ----------- | 2 3 | x + 12*x + 45 | /
$${{\arctan \left({{2\,x+12}\over{6}}\right)}\over{3}}$$
The graph
The answer
[src]
atan(2) atan(7/3)
- ------- + ---------
3 3
$${{\arctan \left({{7}\over{3}}\right)}\over{3}}-{{\arctan 2}\over{3
}}$$
=
=
atan(2) atan(7/3)
- ------- + ---------
3 3
$$- \frac{\operatorname{atan}{\left(2 \right)}}{3} + \frac{\operatorname{atan}{\left(\frac{7}{3} \right)}}{3}$$
The graph
Use the examples entering the upper and lower limits of integration.