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How to use it?
- Integral of d{x}:
-
Integral of e^(-x)*sin(2*x)
-
Integral of xsinx^2
-
Integral of xsin(2x)dx
-
Integral of 1/100
- Equation:
- 1/(64+x^2)
-
Identical expressions
- one /(sixty-four +x^ two)
- 1 divide by (64 plus x squared )
- one divide by (sixty minus four plus x to the power of two)
- 1/(64+x2)
- 1/64+x2
- 1/(64+x²)
- 1/(64+x to the power of 2)
- 1/64+x^2
- 1 divide by (64+x^2)
- 1/(64+x^2)dx
-
Similar expressions
- 1/(64-x^2)
Integral of 1/(64+x^2) dx
The solution
You have entered
[src]
1 / | | 1 | ------- dx | 2 | 64 + x | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{2} + 64}\, dx$$
Integral(1/(64 + x^2), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | ------- dx | 2 | 64 + x | /
Rewrite the integrand
1 1
------- = ---------------
2 / 2 \
64 + x |/-x \ |
64*||---| + 1|
\\ 8 / /or
/ | | 1 | ------- dx | 2 = | 64 + x | /
/
|
| 1
| ---------- dx
| 2
| /-x \
| |---| + 1
| \ 8 /
|
/
----------------
64 In the integral
/
|
| 1
| ---------- dx
| 2
| /-x \
| |---| + 1
| \ 8 /
|
/
----------------
64 do replacement
-x
v = ---
8 then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
64 64 do backward replacement
/
|
| 1
| ---------- dx
| 2
| /-x \
| |---| + 1
| \ 8 / /x\
| atan|-|
/ \8/
---------------- = -------
64 8 Solution is:
/x\
atan|-|
\8/
C + -------
8
The answer (Indefinite)
[src]
/ /x\ | atan|-| | 1 \8/ | ------- dx = C + ------- | 2 8 | 64 + x | /
$$\int \frac{1}{x^{2} + 64}\, dx = C + \frac{\operatorname{atan}{\left(\frac{x}{8} \right)}}{8}$$
The graph
The answer
[src]
atan(1/8)
---------
8
$$\frac{\operatorname{atan}{\left(\frac{1}{8} \right)}}{8}$$
=
=
atan(1/8)
---------
8
$$\frac{\operatorname{atan}{\left(\frac{1}{8} \right)}}{8}$$
atan(1/8)/8
Use the examples entering the upper and lower limits of integration.