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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
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How to use it?
- Integral of d{x}:
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Integral of sinxcos2x
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Integral of (x(x^2-7))/(x^2+2)dx
- Integral of (x^3-1)/(x^4+x^2+5)
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Integral of x^2/sqrt(1+x^4)
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Identical expressions
- sqrt(one +(one / three)*sqrt((2x- one)^ three))
- square root of (1 plus (1 divide by 3) multiply by square root of ((2x minus 1) cubed ))
- square root of (one plus (one divide by three) multiply by square root of ((2x minus one) to the power of three))
- √(1+(1/3)*√((2x-1)^3))
- sqrt(1+(1/3)*sqrt((2x-1)3))
- sqrt1+1/3*sqrt2x-13
- sqrt(1+(1/3)*sqrt((2x-1)³))
- sqrt(1+(1/3)*sqrt((2x-1) to the power of 3))
- sqrt(1+(1/3)sqrt((2x-1)^3))
- sqrt(1+(1/3)sqrt((2x-1)3))
- sqrt1+1/3sqrt2x-13
- sqrt1+1/3sqrt2x-1^3
- sqrt(1+(1 divide by 3)*sqrt((2x-1)^3))
- sqrt(1+(1/3)*sqrt((2x-1)^3))dx
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Similar expressions
- sqrt(1+(1/3)*sqrt((2x+1)^3))
- sqrt(1-(1/3)*sqrt((2x-1)^3))
Integral of sqrt(1+(1/3)*sqrt((2x-1)^3)) dx
The solution
You have entered
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1 / | | _____________________ | / ____________ | / / 3 | / \/ (2*x - 1) | / 1 + --------------- dx | \/ 3 | / 0
$$\int\limits_{0}^{1} \sqrt{\frac{\sqrt{\left(2 x - 1\right)^{3}}}{3} + 1}\, dx$$
Integral(sqrt(1 + sqrt((2*x - 1)^3)/3), (x, 0, 1))
The answer (Indefinite)
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/
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/ | __________________________________
| | / _________________________
| _____________________ ___ | / / 2 3
| / ____________ \/ 3 * | \/ 3 + \/ -1 - 12*x + 6*x + 8*x dx
| / / 3 |
| / \/ (2*x - 1) /
| / 1 + --------------- dx = C + --------------------------------------------------
| \/ 3 3
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$$\int \sqrt{\frac{\sqrt{\left(2 x - 1\right)^{3}}}{3} + 1}\, dx = C + \frac{\sqrt{3} \int \sqrt{\sqrt{8 x^{3} - 12 x^{2} + 6 x - 1} + 3}\, dx}{3}$$
Numerical answer
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(1.03348148310538 + 0.0331290119029962j)
(1.03348148310538 + 0.0331290119029962j)
Use the examples entering the upper and lower limits of integration.