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How to use it?
- Integral of d{x}:
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Integral of x^3*e^x*dx
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Integral of exp(x)/x
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Integral of x*exp(-x^2)
- Integral of x/(x-1)^2
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Identical expressions
- dx/(4x^ two - nine)
- dx divide by (4x squared minus 9)
- dx divide by (4x to the power of two minus nine)
- dx/(4x2-9)
- dx/4x2-9
- dx/(4x²-9)
- dx/(4x to the power of 2-9)
- dx/4x^2-9
- dx divide by (4x^2-9)
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Similar expressions
- dx/(4x^2+9)
Integral of dx/(4x^2-9) dx
The solution
You have entered
[src]
1 / | | 1 | -------- dx | 2 | 4*x - 9 | / 0
$$\int\limits_{0}^{1} \frac{1}{4 x^{2} - 9}\, dx$$
Integral(1/(4*x^2 - 9), (x, 0, 1))
Detail solution
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Add the constant of integration:
PiecewiseRule(subfunctions=[(ArctanRule(a=1, b=4, c=-9, context=1/(4*x**2 - 9), symbol=x), False), (ArccothRule(a=1, b=4, c=-9, context=1/(4*x**2 - 9), symbol=x), x**2 > 9/4), (ArctanhRule(a=1, b=4, c=-9, context=1/(4*x**2 - 9), symbol=x), x**2 < 9/4)], context=1/(4*x**2 - 9), symbol=x)
The answer is:
The answer (Indefinite)
[src]
// /2*x\ \
||-acoth|---| |
/ || \ 3 / 2 |
| ||------------ for x > 9/4|
| 1 || 6 |
| -------- dx = C + |< |
| 2 || /2*x\ |
| 4*x - 9 ||-atanh|---| |
| || \ 3 / 2 |
/ ||------------ for x < 9/4|
\\ 6 /
$$\int \frac{1}{4 x^{2} - 9}\, dx = C + \begin{cases} - \frac{\operatorname{acoth}{\left(\frac{2 x}{3} \right)}}{6} & \text{for}\: x^{2} > \frac{9}{4} \\- \frac{\operatorname{atanh}{\left(\frac{2 x}{3} \right)}}{6} & \text{for}\: x^{2} < \frac{9}{4} \end{cases}$$
The graph
The answer
[src]
log(2) log(5/2)
- ------ - --------
12 12
$$- \frac{\log{\left(\frac{5}{2} \right)}}{12} - \frac{\log{\left(2 \right)}}{12}$$
=
=
log(2) log(5/2)
- ------ - --------
12 12
$$- \frac{\log{\left(\frac{5}{2} \right)}}{12} - \frac{\log{\left(2 \right)}}{12}$$
-log(2)/12 - log(5/2)/12
The graph
Use the examples entering the upper and lower limits of integration.