Mister Exam
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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of 1/(lnx)
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Integral of x^2/(1+x^2)^2
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Integral of e^(2x+3)
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Integral of dx/(2+x^2)
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Identical expressions
- one /(a^ two -x^ two)
- 1 divide by (a squared minus x squared )
- one divide by (a to the power of two minus x to the power of two)
- 1/(a2-x2)
- 1/a2-x2
- 1/(a²-x²)
- 1/(a to the power of 2-x to the power of 2)
- 1/a^2-x^2
- 1 divide by (a^2-x^2)
- 1/(a^2-x^2)dx
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Similar expressions
- 1/(a^2+x^2)
Integral of 1/(a^2-x^2) dx
The solution
You have entered
[src]
1 / | | 1 | ------- dx | 2 2 | a - x | / 0
$$\int\limits_{0}^{1} \frac{1}{a^{2} - x^{2}}\, dx$$
Integral(1/(a^2 - x^2), (x, 0, 1))
Detail solution
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The integral of is .
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Add the constant of integration:
The answer is:
The answer (Indefinite)
[src]
/ x \
atan|--------|
/ | _____|
| | / 2 |
| 1 \\/ -a /
| ------- dx = C - --------------
| 2 2 _____
| a - x / 2
| \/ -a
/
$$\int \frac{1}{a^{2} - x^{2}}\, dx = C - \frac{\operatorname{atan}{\left(\frac{x}{\sqrt{- a^{2}}} \right)}}{\sqrt{- a^{2}}}$$
The answer
[src]
log(-a) log(a) log(1 - a) log(1 + a)
------- - ------ ---------- - ----------
2 2 2 2
---------------- - -----------------------
a a
$$\frac{\frac{\log{\left(- a \right)}}{2} - \frac{\log{\left(a \right)}}{2}}{a} - \frac{\frac{\log{\left(1 - a \right)}}{2} - \frac{\log{\left(a + 1 \right)}}{2}}{a}$$
=
=
log(-a) log(a) log(1 - a) log(1 + a)
------- - ------ ---------- - ----------
2 2 2 2
---------------- - -----------------------
a a
$$\frac{\frac{\log{\left(- a \right)}}{2} - \frac{\log{\left(a \right)}}{2}}{a} - \frac{\frac{\log{\left(1 - a \right)}}{2} - \frac{\log{\left(a + 1 \right)}}{2}}{a}$$
(log(-a)/2 - log(a)/2)/a - (log(1 - a)/2 - log(1 + a)/2)/a
Use the examples entering the upper and lower limits of integration.