Mister Exam
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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
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-
How to use it?
- Integral of d{x}:
-
Integral of (x^2+1)/((x^3+3x+1)^5)
-
Integral of sqrt(x^2-9)/x
- Integral of ln(ln(x))/x
- Integral of sin(w*t)^2
-
Identical expressions
- t/(two *(t^ two - one))
- t divide by (2 multiply by (t squared minus 1))
- t divide by (two multiply by (t to the power of two minus one))
- t/(2*(t2-1))
- t/2*t2-1
- t/(2*(t²-1))
- t/(2*(t to the power of 2-1))
- t/(2(t^2-1))
- t/(2(t2-1))
- t/2t2-1
- t/2t^2-1
- t divide by (2*(t^2-1))
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Similar expressions
- t/(2*(t^2+1))
Integral of t/(2*(t^2-1)) dx
The solution
You have entered
[src]
3 / | | t | ---------- dt | / 2 \ | 2*\t - 1/ | / 2
$$\int\limits_{2}^{3} \frac{t}{2 \left(t^{2} - 1\right)}\, dt$$
Integral(t/((2*(t^2 - 1))), (t, 2, 3))
Detail solution
We have the integral:
/ | | t | ---------- dt | / 2 \ | 2*\t - 1/ | /
Rewrite the integrand
/ 2*2*t \
|--------------|
| 2 |
t \2*t + 0*t - 2/
---------- = ----------------
/ 2 \ 4
2*\t - 1/ or
/ | | t | ---------- dt | / 2 \ = | 2*\t - 1/ | /
/
|
| 2*2*t
| -------------- dt
| 2
| 2*t + 0*t - 2
|
/
--------------------
4 In the integral
/
|
| 2*2*t
| -------------- dt
| 2
| 2*t + 0*t - 2
|
/
--------------------
4 do replacement
2 u = 2*t
then
the integral =
/
|
| 1
| ------ du
| -2 + u
|
/ log(-2 + u)
------------ = -----------
4 4 do backward replacement
/
|
| 2*2*t
| -------------- dt
| 2
| 2*t + 0*t - 2
| / 2\
/ log\-1 + t /
-------------------- = ------------
4 4 Solution is:
/ 2\
log\-1 + t /
C + ------------
4
The answer (Indefinite)
[src]
/ | | t log(1 + t) log(-1 + t) | ---------- dt = C + ---------- + ----------- | / 2 \ 4 4 | 2*\t - 1/ | /
$$\int \frac{t}{2 \left(t^{2} - 1\right)}\, dt = C + \frac{\log{\left(t - 1 \right)}}{4} + \frac{\log{\left(t + 1 \right)}}{4}$$
The graph
The answer
[src]
log(3) log(8)
- ------ + ------
4 4
$$- \frac{\log{\left(3 \right)}}{4} + \frac{\log{\left(8 \right)}}{4}$$
=
=
log(3) log(8)
- ------ + ------
4 4
$$- \frac{\log{\left(3 \right)}}{4} + \frac{\log{\left(8 \right)}}{4}$$
-log(3)/4 + log(8)/4
Use the examples entering the upper and lower limits of integration.