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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x^(-1/2)
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Integral of 1/sqrt(1+u^2)
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Integral of x^4lnx
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Integral of x*dx/(x^2-1)
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Identical expressions
- dx/(sqrt(four - five *x^ two))
- dx divide by ( square root of (4 minus 5 multiply by x squared ))
- dx divide by ( square root of (four minus five multiply by x to the power of two))
- dx/(√(4-5*x^2))
- dx/(sqrt(4-5*x2))
- dx/sqrt4-5*x2
- dx/(sqrt(4-5*x²))
- dx/(sqrt(4-5*x to the power of 2))
- dx/(sqrt(4-5x^2))
- dx/(sqrt(4-5x2))
- dx/sqrt4-5x2
- dx/sqrt4-5x^2
- dx divide by (sqrt(4-5*x^2))
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Similar expressions
- dx/(sqrt(4+5*x^2))
Integral of dx/(sqrt(4-5*x^2)) dx
The solution
You have entered
[src]
1 / | | 1 | ------------- dx | __________ | / 2 | \/ 4 - 5*x | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{4 - 5 x^{2}}}\, dx$$
Integral(1/(sqrt(4 - 5*x^2)), (x, 0, 1))
Detail solution
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Add the constant of integration:
TrigSubstitutionRule(theta=_theta, func=2*sqrt(5)*sin(_theta)/5, rewritten=sqrt(5)/5, substep=ConstantRule(constant=sqrt(5)/5, context=sqrt(5)/5, symbol=_theta), restriction=(x > -2*sqrt(5)/5) & (x < 2*sqrt(5)/5), context=1/(sqrt(4 - 5*x**2)), symbol=x)
The answer is:
The answer (Indefinite)
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/ // / ___\ \ | || ___ |x*\/ 5 | | | 1 ||\/ 5 *asin|-------| / ___ ___\| | ------------- dx = C + |< \ 2 / | -2*\/ 5 2*\/ 5 || | __________ ||------------------- for And|x > --------, x < -------|| | / 2 || 5 \ 5 5 /| | \/ 4 - 5*x \\ / | /
$$\int \frac{1}{\sqrt{4 - 5 x^{2}}}\, dx = C + \begin{cases} \frac{\sqrt{5} \operatorname{asin}{\left(\frac{\sqrt{5} x}{2} \right)}}{5} & \text{for}\: x > - \frac{2 \sqrt{5}}{5} \wedge x < \frac{2 \sqrt{5}}{5} \end{cases}$$
The graph
The answer
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/ ___\
___ |\/ 5 |
\/ 5 *asin|-----|
\ 2 /
-----------------
5
$$\frac{\sqrt{5} \operatorname{asin}{\left(\frac{\sqrt{5}}{2} \right)}}{5}$$
=
=
/ ___\
___ |\/ 5 |
\/ 5 *asin|-----|
\ 2 /
-----------------
5
$$\frac{\sqrt{5} \operatorname{asin}{\left(\frac{\sqrt{5}}{2} \right)}}{5}$$
sqrt(5)*asin(sqrt(5)/2)/5
Numerical answer
[src]
(0.676056261612884 - 0.21818552482013j)
(0.676056261612884 - 0.21818552482013j)
Use the examples entering the upper and lower limits of integration.