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- Integral of d{x}:
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Integral of 4*x*exp(x^2)
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Integral of sen4x
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Integral of sqrt(x^2+4)
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Integral of dx/(x^2+7)
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Identical expressions
- dx/(x^ two + seven)
- dx divide by (x squared plus 7)
- dx divide by (x to the power of two plus seven)
- dx/(x2+7)
- dx/x2+7
- dx/(x²+7)
- dx/(x to the power of 2+7)
- dx/x^2+7
- dx divide by (x^2+7)
-
Similar expressions
- dx/(x^2-7)
Integral of dx/(x^2+7) dx
The solution
You have entered
[src]
1 / | | 1 | ------ dx | 2 | x + 7 | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{2} + 7}\, dx$$
Integral(1/(x^2 + 7), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | ------ dx | 2 | x + 7 | /
Rewrite the integrand
1 1
------ = --------------------
2 / 2 \
x + 7 |/ ___ \ |
||-\/ 7 | |
7*||-------*x| + 1|
\\ 7 / /or
/ | | 1 | ------ dx | 2 = | x + 7 | /
/
|
| 1
| ---------------- dx
| 2
| / ___ \
| |-\/ 7 |
| |-------*x| + 1
| \ 7 /
|
/
----------------------
7 In the integral
/
|
| 1
| ---------------- dx
| 2
| / ___ \
| |-\/ 7 |
| |-------*x| + 1
| \ 7 /
|
/
----------------------
7 do replacement
___
-x*\/ 7
v = ---------
7 then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
7 7 do backward replacement
/
|
| 1
| ---------------- dx
| 2
| / ___ \
| |-\/ 7 |
| |-------*x| + 1 / ___\
| \ 7 / ___ |x*\/ 7 |
| \/ 7 *atan|-------|
/ \ 7 /
---------------------- = -------------------
7 7 Solution is:
/ ___\
___ |x*\/ 7 |
\/ 7 *atan|-------|
\ 7 /
C + -------------------
7
The answer (Indefinite)
[src]
/ ___\ / ___ |x*\/ 7 | | \/ 7 *atan|-------| | 1 \ 7 / | ------ dx = C + ------------------- | 2 7 | x + 7 | /
$$\int \frac{1}{x^{2} + 7}\, dx = C + \frac{\sqrt{7} \operatorname{atan}{\left(\frac{\sqrt{7} x}{7} \right)}}{7}$$
The graph
The answer
[src]
/ ___\
___ |\/ 7 |
\/ 7 *atan|-----|
\ 7 /
-----------------
7
$$\frac{\sqrt{7} \operatorname{atan}{\left(\frac{\sqrt{7}}{7} \right)}}{7}$$
=
=
/ ___\
___ |\/ 7 |
\/ 7 *atan|-----|
\ 7 /
-----------------
7
$$\frac{\sqrt{7} \operatorname{atan}{\left(\frac{\sqrt{7}}{7} \right)}}{7}$$
sqrt(7)*atan(sqrt(7)/7)/7
The graph
Use the examples entering the upper and lower limits of integration.