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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of e^x/x^2
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Integral of sin(x)^2*cos(x)^4
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Integral of x*ln(x+1)dx
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Integral of 1/(2-x)
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Identical expressions
- xdx/(sqrt(one -x^ four))
- xdx divide by ( square root of (1 minus x to the power of 4))
- xdx divide by ( square root of (one minus x to the power of four))
- xdx/(√(1-x^4))
- xdx/(sqrt(1-x4))
- xdx/sqrt1-x4
- xdx/(sqrt(1-x⁴))
- xdx/sqrt1-x^4
- xdx divide by (sqrt(1-x^4))
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Similar expressions
- xdx/(sqrt(1+x^4))
- sqrt(x)*dx/sqrt(1-x^4)
Integral of xdx/(sqrt(1-x^4)) dx
The solution
You have entered
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1 / | | x | ----------- dx | ________ | / 4 | \/ 1 - x | / 0
$$\int\limits_{0}^{1} \frac{x}{\sqrt{1 - x^{4}}}\, dx$$
Integral(x/sqrt(1 - x^4), (x, 0, 1))
The answer (Indefinite)
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// / 2\ \ / ||-I*acosh\x / | 4| | | ||------------- for |x | > 1| | x || 2 | | ----------- dx = C + |< | | ________ || / 2\ | | / 4 || asin\x / | | \/ 1 - x || -------- otherwise | | \\ 2 / /
$$\int \frac{x}{\sqrt{1 - x^{4}}}\, dx = C + \begin{cases} - \frac{i \operatorname{acosh}{\left(x^{2} \right)}}{2} & \text{for}\: \left|{x^{4}}\right| > 1 \\\frac{\operatorname{asin}{\left(x^{2} \right)}}{2} & \text{otherwise} \end{cases}$$
The graph
The answer
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1 / | | / -I*x 4 | |------------ for x > 1 | | _________ | | / 4 | |\/ -1 + x | < dx | | x | |----------- otherwise | | ________ | | / 4 | \\/ 1 - x | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x}{\sqrt{x^{4} - 1}} & \text{for}\: x^{4} > 1 \\\frac{x}{\sqrt{1 - x^{4}}} & \text{otherwise} \end{cases}\, dx$$
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1 / | | / -I*x 4 | |------------ for x > 1 | | _________ | | / 4 | |\/ -1 + x | < dx | | x | |----------- otherwise | | ________ | | / 4 | \\/ 1 - x | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x}{\sqrt{x^{4} - 1}} & \text{for}\: x^{4} > 1 \\\frac{x}{\sqrt{1 - x^{4}}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((-i*x/sqrt(-1 + x^4), x^4 > 1), (x/sqrt(1 - x^4), True)), (x, 0, 1))
The graph
Use the examples entering the upper and lower limits of integration.