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- Improper integral
- Double Integral
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- Curvilinear integral
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How to use it?
- Integral of d{x}:
-
Integral of sqrt(1+x^2)/x^2
-
Integral of ln(1+x^2)dx
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Integral of cos^2(x)dx
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Integral of dx/(2-3*x)
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Identical expressions
- one /(81x^ two + sixteen)
- 1 divide by (81x squared plus 16)
- one divide by (81x to the power of two plus sixteen)
- 1/(81x2+16)
- 1/81x2+16
- 1/(81x²+16)
- 1/(81x to the power of 2+16)
- 1/81x^2+16
- 1 divide by (81x^2+16)
- 1/(81x^2+16)dx
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Similar expressions
- 1/(81x^2-16)
Integral of 1/(81x^2+16) dx
The solution
You have entered
[src]
1 / | | 1 | 1*---------- dx | 2 | 81*x + 16 | / 0
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{81 x^{2} + 16}\, dx$$
Integral(1/(81*x^2 + 16), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | 1*1*---------- dx | 2 | 81*x + 16 | /
Rewrite the integrand
1 1
1*---------- = ---------------------
2 / 2 \
81*x + 16 |/ 9*x \ |
16*||- --- + 0| + 1|
\\ 4 / /or
/ | | 1 | 1*1*---------- dx | 2 = | 81*x + 16 | /
/
|
| 1
| ---------------- dx
| 2
| / 9*x \
| |- --- + 0| + 1
| \ 4 /
|
/
----------------------
16 In the integral
/
|
| 1
| ---------------- dx
| 2
| / 9*x \
| |- --- + 0| + 1
| \ 4 /
|
/
----------------------
16 do replacement
-9*x
v = ----
4 then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
16 16 do backward replacement
/
|
| 1
| ---------------- dx
| 2
| / 9*x \
| |- --- + 0| + 1
| \ 4 / /9*x\
| atan|---|
/ \ 4 /
---------------------- = ---------
16 36 Solution is:
/9*x\
atan|---|
\ 4 /
C + ---------
36
The answer (Indefinite)
[src]
/ /9*x\ | atan|---| | 1 \ 4 / | 1*---------- dx = C + --------- | 2 36 | 81*x + 16 | /
$${{\arctan \left({{9\,x}\over{4}}\right)}\over{36}}$$
The graph
The answer
[src]
atan(9/4)
---------
36
$${{\arctan \left({{9}\over{4}}\right)}\over{36}}$$
=
=
atan(9/4)
---------
36
$$\frac{\operatorname{atan}{\left(\frac{9}{4} \right)}}{36}$$
The graph
Use the examples entering the upper and lower limits of integration.