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How to use it?
- Integral of d{x}:
-
Integral of x^3*e^(x^4)
-
Integral of (x^2+1)e^-x
-
Integral of 1/sqrt(1-y^2)
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Integral of x/(x^2+4)^(1/2)
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Identical expressions
- one /(x^ two +8x+ twenty-five)
- 1 divide by (x squared plus 8x plus 25)
- one divide by (x to the power of two plus 8x plus twenty minus five)
- 1/(x2+8x+25)
- 1/x2+8x+25
- 1/(x²+8x+25)
- 1/(x to the power of 2+8x+25)
- 1/x^2+8x+25
- 1 divide by (x^2+8x+25)
- 1/(x^2+8x+25)dx
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Similar expressions
- 1/(x^2+8x-25)
- 1/(x^2-8x+25)
Integral of 1/(x^2+8x+25) dx
The solution
You have entered
[src]
2 / | | 1 | ------------- dx | 2 | x + 8*x + 25 | / 0
$$\int\limits_{0}^{2} \frac{1}{\left(x^{2} + 8 x\right) + 25}\, dx$$
Integral(1/(x^2 + 8*x + 25), (x, 0, 2))
Detail solution
We have the integral:
/ | | 1 | ------------- dx | 2 | x + 8*x + 25 | /
Rewrite the integrand
1 1
------------- = ------------------
2 / 2 \
x + 8*x + 25 |/ x 4\ |
9*||- - - -| + 1|
\\ 3 3/ /or
/ | | 1 | ------------- dx | 2 = | x + 8*x + 25 | /
/
|
| 1
| -------------- dx
| 2
| / x 4\
| |- - - -| + 1
| \ 3 3/
|
/
--------------------
9 In the integral
/
|
| 1
| -------------- dx
| 2
| / x 4\
| |- - - -| + 1
| \ 3 3/
|
/
--------------------
9 do replacement
4 x
v = - - - -
3 3then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
9 9 do backward replacement
/
|
| 1
| -------------- dx
| 2
| / x 4\
| |- - - -| + 1
| \ 3 3/ /4 x\
| atan|- + -|
/ \3 3/
-------------------- = -----------
9 3 Solution is:
/4 x\
atan|- + -|
\3 3/
C + -----------
3
The answer (Indefinite)
[src]
/ /4 x\ | atan|- + -| | 1 \3 3/ | ------------- dx = C + ----------- | 2 3 | x + 8*x + 25 | /
$$\int \frac{1}{\left(x^{2} + 8 x\right) + 25}\, dx = C + \frac{\operatorname{atan}{\left(\frac{x}{3} + \frac{4}{3} \right)}}{3}$$
The graph
The answer
[src]
atan(4/3) atan(2)
- --------- + -------
3 3
$$- \frac{\operatorname{atan}{\left(\frac{4}{3} \right)}}{3} + \frac{\operatorname{atan}{\left(2 \right)}}{3}$$
=
=
atan(4/3) atan(2)
- --------- + -------
3 3
$$- \frac{\operatorname{atan}{\left(\frac{4}{3} \right)}}{3} + \frac{\operatorname{atan}{\left(2 \right)}}{3}$$
-atan(4/3)/3 + atan(2)/3
Use the examples entering the upper and lower limits of integration.