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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×e^x
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Integral of e^(x*(-4))
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Integral of x^2e^x
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Integral of (x*x)*exp(-x/2)
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Identical expressions
- dx/sqrt(seven -4x^ two)
- dx divide by square root of (7 minus 4x squared )
- dx divide by square root of (seven minus 4x to the power of two)
- dx/√(7-4x^2)
- dx/sqrt(7-4x2)
- dx/sqrt7-4x2
- dx/sqrt(7-4x²)
- dx/sqrt(7-4x to the power of 2)
- dx/sqrt7-4x^2
- dx divide by sqrt(7-4x^2)
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Similar expressions
- dx/sqrt(7+4x^2)
Integral of dx/sqrt(7-4x^2) dx
The solution
You have entered
[src]
1 / | | 1 | ------------- dx | __________ | / 2 | \/ 7 - 4*x | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{7 - 4 x^{2}}}\, dx$$
Integral(1/(sqrt(7 - 4*x^2)), (x, 0, 1))
Detail solution
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Add the constant of integration:
TrigSubstitutionRule(theta=_theta, func=sqrt(7)*sin(_theta)/2, rewritten=1/2, substep=ConstantRule(constant=1/2, context=1/2, symbol=_theta), restriction=(x > -sqrt(7)/2) & (x < sqrt(7)/2), context=1/(sqrt(7 - 4*x**2)), symbol=x)
The answer is:
The answer (Indefinite)
[src]
/ // / ___\ \ | || |2*x*\/ 7 | | | 1 ||asin|---------| / ___ ___\| | ------------- dx = C + |< \ 7 / | -\/ 7 \/ 7 || | __________ ||--------------- for And|x > -------, x < -----|| | / 2 || 2 \ 2 2 /| | \/ 7 - 4*x \\ / | /
$$\int \frac{1}{\sqrt{7 - 4 x^{2}}}\, dx = C + \begin{cases} \frac{\operatorname{asin}{\left(\frac{2 \sqrt{7} x}{7} \right)}}{2} & \text{for}\: x > - \frac{\sqrt{7}}{2} \wedge x < \frac{\sqrt{7}}{2} \end{cases}$$
The graph
The answer
[src]
/ ___\
|2*\/ 7 |
asin|-------|
\ 7 /
-------------
2
$$\frac{\operatorname{asin}{\left(\frac{2 \sqrt{7}}{7} \right)}}{2}$$
=
=
/ ___\
|2*\/ 7 |
asin|-------|
\ 7 /
-------------
2
$$\frac{\operatorname{asin}{\left(\frac{2 \sqrt{7}}{7} \right)}}{2}$$
asin(2*sqrt(7)/7)/2
Use the examples entering the upper and lower limits of integration.