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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^(3*x)
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Integral of 3/x
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Integral of x/(x+1)
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Integral of x*ln(x)
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Identical expressions
- sqrt(one +(sqrt(six (x- one))^ three)/(two (x- one)))
- square root of (1 plus ( square root of (6(x minus 1)) cubed ) divide by (2(x minus 1)))
- square root of (one plus ( square root of (six (x minus one)) to the power of three) divide by (two (x minus one)))
- √(1+(√(6(x-1))^3)/(2(x-1)))
- sqrt(1+(sqrt(6(x-1))3)/(2(x-1)))
- sqrt1+sqrt6x-13/2x-1
- sqrt(1+(sqrt(6(x-1))³)/(2(x-1)))
- sqrt(1+(sqrt(6(x-1)) to the power of 3)/(2(x-1)))
- sqrt1+sqrt6x-1^3/2x-1
- sqrt(1+(sqrt(6(x-1))^3) divide by (2(x-1)))
- sqrt(1+(sqrt(6(x-1))^3)/(2(x-1)))dx
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Similar expressions
- sqrt(1-(sqrt(6(x-1))^3)/(2(x-1)))
- sqrt(1+(sqrt(6(x+1))^3)/(2(x-1)))
- sqrt(1+(sqrt(6(x-1))^3)/(2(x+1)))
Integral of sqrt(1+(sqrt(6(x-1))^3)/(2(x-1))) dx
The solution
You have entered
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3 / | | ____________________ | / 3 | / ___________ | / \/ 6*(x - 1) | / 1 + -------------- dx | \/ 2*(x - 1) | / 1
$$\int\limits_{1}^{3} \sqrt{\frac{\left(\sqrt{6 \left(x - 1\right)}\right)^{3}}{2 \left(x - 1\right)} + 1}\, dx$$
Integral(sqrt(1 + (sqrt(6*(x - 1)))^3/((2*(x - 1)))), (x, 1, 3))
The answer (Indefinite)
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/ | | ____________________ | / 3 ________________________ ________________________ ________________________ ________________________ | / ___________ 2 / ___ ________ 2 ___ 5/2 / ___ ________ 3 ___ / ___ ________ 5/2 ___ / ___ ________ 7/2 | / \/ 6*(x - 1) 4*(-1 + x) 4*\/ 1 + 3*\/ 6 *\/ -1 + x *(-1 + x) 12*\/ 6 *(-1 + x) 432*\/ 1 + 3*\/ 6 *\/ -1 + x *(-1 + x) 6*\/ 6 *\/ 1 + 3*\/ 6 *\/ -1 + x *(-1 + x) 972*\/ 6 *\/ 1 + 3*\/ 6 *\/ -1 + x *(-1 + x) | / 1 + -------------- dx = C + -------------------------------------- - --------------------------------------- + -------------------------------------- + ----------------------------------------- - ----------------------------------------------- + ------------------------------------------------- | \/ 2*(x - 1) 2 ___ 5/2 2 ___ 5/2 2 ___ 5/2 2 ___ 5/2 2 ___ 5/2 2 ___ 5/2 | 405*(-1 + x) + 1215*\/ 6 *(-1 + x) 405*(-1 + x) + 1215*\/ 6 *(-1 + x) 405*(-1 + x) + 1215*\/ 6 *(-1 + x) 405*(-1 + x) + 1215*\/ 6 *(-1 + x) 405*(-1 + x) + 1215*\/ 6 *(-1 + x) 405*(-1 + x) + 1215*\/ 6 *(-1 + x) /
$$\int \sqrt{\frac{\left(\sqrt{6 \left(x - 1\right)}\right)^{3}}{2 \left(x - 1\right)} + 1}\, dx = C + \frac{972 \sqrt{6} \left(x - 1\right)^{\frac{7}{2}} \sqrt{3 \sqrt{6} \sqrt{x - 1} + 1}}{1215 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}} + 405 \left(x - 1\right)^{2}} - \frac{6 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}} \sqrt{3 \sqrt{6} \sqrt{x - 1} + 1}}{1215 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}} + 405 \left(x - 1\right)^{2}} + \frac{12 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}}}{1215 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}} + 405 \left(x - 1\right)^{2}} + \frac{432 \left(x - 1\right)^{3} \sqrt{3 \sqrt{6} \sqrt{x - 1} + 1}}{1215 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}} + 405 \left(x - 1\right)^{2}} - \frac{4 \left(x - 1\right)^{2} \sqrt{3 \sqrt{6} \sqrt{x - 1} + 1}}{1215 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}} + 405 \left(x - 1\right)^{2}} + \frac{4 \left(x - 1\right)^{2}}{1215 \sqrt{6} \left(x - 1\right)^{\frac{5}{2}} + 405 \left(x - 1\right)^{2}}$$
The graph
The answer
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_____________ _____________
___ / ___ ___ / ___
16 96*\/ 3 3440*\/ 1 + 6*\/ 3 15504*\/ 3 *\/ 1 + 6*\/ 3
----------------- + ----------------- + --------------------- + ----------------------------
___ ___ ___ ___
1620 + 9720*\/ 3 1620 + 9720*\/ 3 1620 + 9720*\/ 3 1620 + 9720*\/ 3
$$\frac{16}{1620 + 9720 \sqrt{3}} + \frac{96 \sqrt{3}}{1620 + 9720 \sqrt{3}} + \frac{3440 \sqrt{1 + 6 \sqrt{3}}}{1620 + 9720 \sqrt{3}} + \frac{15504 \sqrt{3} \sqrt{1 + 6 \sqrt{3}}}{1620 + 9720 \sqrt{3}}$$
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_____________ _____________
___ / ___ ___ / ___
16 96*\/ 3 3440*\/ 1 + 6*\/ 3 15504*\/ 3 *\/ 1 + 6*\/ 3
----------------- + ----------------- + --------------------- + ----------------------------
___ ___ ___ ___
1620 + 9720*\/ 3 1620 + 9720*\/ 3 1620 + 9720*\/ 3 1620 + 9720*\/ 3
$$\frac{16}{1620 + 9720 \sqrt{3}} + \frac{96 \sqrt{3}}{1620 + 9720 \sqrt{3}} + \frac{3440 \sqrt{1 + 6 \sqrt{3}}}{1620 + 9720 \sqrt{3}} + \frac{15504 \sqrt{3} \sqrt{1 + 6 \sqrt{3}}}{1620 + 9720 \sqrt{3}}$$
16/(1620 + 9720*sqrt(3)) + 96*sqrt(3)/(1620 + 9720*sqrt(3)) + 3440*sqrt(1 + 6*sqrt(3))/(1620 + 9720*sqrt(3)) + 15504*sqrt(3)*sqrt(1 + 6*sqrt(3))/(1620 + 9720*sqrt(3))
Use the examples entering the upper and lower limits of integration.