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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of e^(x^4)*x^3
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Integral of sinxcos2x
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Integral of cos4x/sin^34x
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Integral of 9/(x^2+9)
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Identical expressions
- nine /(x^ two + nine)
- 9 divide by (x squared plus 9)
- nine divide by (x to the power of two plus nine)
- 9/(x2+9)
- 9/x2+9
- 9/(x²+9)
- 9/(x to the power of 2+9)
- 9/x^2+9
- 9 divide by (x^2+9)
- 9/(x^2+9)dx
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Similar expressions
- 9/(x^2-9)
Integral of 9/(x^2+9) dx
The solution
You have entered
[src]
1 / | | 9 | ------ dx | 2 | x + 9 | / 0
$$\int\limits_{0}^{1} \frac{9}{x^{2} + 9}\, dx$$
Integral(9/(x^2 + 9), (x, 0, 1))
Detail solution
We have the integral:
/ | | 9 | ------ dx | 2 | x + 9 | /
Rewrite the integrand
/9\
|-|
9 \9/
------ = ----------
2 2
x + 9 /-x \
|---| + 1
\ 3 / or
/ | | 9 | ------ dx | 2 = | x + 9 | /
/ | | 1 | ---------- dx | 2 | /-x \ | |---| + 1 | \ 3 / | /
In the integral
/ | | 1 | ---------- dx | 2 | /-x \ | |---| + 1 | \ 3 / | /
do replacement
-x
v = ---
3 then
the integral =
/ | | 1 | ------ dv = atan(v) | 2 | 1 + v | /
do backward replacement
/ | | 1 /x\ | ---------- dx = 3*atan|-| | 2 \3/ | /-x \ | |---| + 1 | \ 3 / | /
Solution is:
/x\
C + 3*atan|-|
\3/
The answer (Indefinite)
[src]
/ | | 9 /x\ | ------ dx = C + 3*atan|-| | 2 \3/ | x + 9 | /
$$\int \frac{9}{x^{2} + 9}\, dx = C + 3 \operatorname{atan}{\left(\frac{x}{3} \right)}$$
The graph
The answer
[src]
3*atan(1/3)
$$3 \operatorname{atan}{\left(\frac{1}{3} \right)}$$
=
=
3*atan(1/3)
$$3 \operatorname{atan}{\left(\frac{1}{3} \right)}$$
3*atan(1/3)
The graph
Use the examples entering the upper and lower limits of integration.