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How to use it?
- Integral of d{x}:
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Integral of x×e^x
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Integral of 1/(x²+1)
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Integral of 1/√(1-4x^2)
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Integral of f(x)=4x
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Identical expressions
- x/(four *x^ two + one)
- x divide by (4 multiply by x squared plus 1)
- x divide by (four multiply by x to the power of two plus one)
- x/(4*x2+1)
- x/4*x2+1
- x/(4*x²+1)
- x/(4*x to the power of 2+1)
- x/(4x^2+1)
- x/(4x2+1)
- x/4x2+1
- x/4x^2+1
- x divide by (4*x^2+1)
- x/(4*x^2+1)dx
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Similar expressions
- x/(4*x^2-1)
Integral of x/(4*x^2+1) dx
The solution
You have entered
[src]
1 / | | x | -------- dx | 2 | 4*x + 1 | / 0
$$\int\limits_{0}^{1} \frac{x}{4 x^{2} + 1}\, dx$$
Integral(x/(4*x^2 + 1), (x, 0, 1))
Detail solution
We have the integral:
/ | | x | 1*-------- dx | 2 | 4*x + 1 | /
Rewrite the integrand
/ 4*2*x + 0 \
|--------------| /0\
| 2 | |-|
x \4*x + 0*x + 1/ \1/
-------- = ---------------- + ---------------
2 8 2
4*x + 1 (-2*x + 0) + 1or
/ | | x | 1*-------- dx | 2 = | 4*x + 1 | /
/
|
| 4*2*x + 0
| -------------- dx
| 2
| 4*x + 0*x + 1
|
/
--------------------
8 In the integral
/
|
| 4*2*x + 0
| -------------- dx
| 2
| 4*x + 0*x + 1
|
/
--------------------
8 do replacement
2 u = 4*x
then
the integral =
/
|
| 1
| ----- du
| 1 + u
|
/ log(1 + u)
----------- = ----------
8 8 do backward replacement
/
|
| 4*2*x + 0
| -------------- dx
| 2
| 4*x + 0*x + 1
| / 2\
/ log\1 + 4*x /
-------------------- = -------------
8 8 In the integral
0
do replacement
v = -2*x
then
the integral =
0 = 0
do backward replacement
0 = 0
Solution is:
/ 2\
log\1 + 4*x /
C + -------------
8
The answer (Indefinite)
[src]
/ | / 2\ | x log\1 + 4*x / | -------- dx = C + ------------- | 2 8 | 4*x + 1 | /
$${{\log \left(4\,x^2+1\right)}\over{8}}$$
The graph
The answer
[src]
log(5) ------ 8
$${{\log 5}\over{8}}$$
=
=
log(5) ------ 8
$$\frac{\log{\left(5 \right)}}{8}$$
The graph
Use the examples entering the upper and lower limits of integration.