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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of xsqrt(x²+1)
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Integral of (x+3)/(x^2-5x+6)
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Integral of (x^3-1)^1/2
- Integral of (sin(2x)+cos(2x))/(1+tg(x))
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Identical expressions
- sqrt(4x^ two -24x+ thirty-seven)
- square root of (4x squared minus 24x plus 37)
- square root of (4x to the power of two minus 24x plus thirty minus seven)
- √(4x^2-24x+37)
- sqrt(4x2-24x+37)
- sqrt4x2-24x+37
- sqrt(4x²-24x+37)
- sqrt(4x to the power of 2-24x+37)
- sqrt4x^2-24x+37
- sqrt(4x^2-24x+37)dx
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Similar expressions
- sqrt(4x^2+24x+37)
- sqrt(4x^2-24x-37)
Integral of sqrt(4x^2-24x+37) dx
The solution
You have entered
[src]
4 / | | __________________ | / 2 | \/ 4*x - 24*x + 37 dx | / 0
$$\int\limits_{0}^{4} \sqrt{4 x^{2} - 24 x + 37}\, dx$$
Integral(sqrt(4*x^2 - 24*x + 37), (x, 0, 4))
Detail solution
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Now simplify:
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Add the constant of integration:
SqrtQuadraticRule(a=37, b=-24, c=4, context=sqrt(4*x**2 - 24*x + 37), symbol=x)
The answer is:
The answer (Indefinite)
[src]
/ | | __________________ __________________ | / 2 asinh(-6 + 2*x) / 2 / 3 x\ | \/ 4*x - 24*x + 37 dx = C + --------------- + \/ 37 - 24*x + 4*x *|- - + -| | 4 \ 2 2/ /
$${{{\rm asinh}\; \left({{8\,x-24}\over{4}}\right)}\over{4}}+{{x\,
\sqrt{4\,x^2-24\,x+37}}\over{2}}-{{3\,\sqrt{4\,x^2-24\,x+37}}\over{2
}}$$
The graph
The answer
[src]
___ ____ \/ 5 asinh(2) asinh(6) 3*\/ 37 ----- + -------- + -------- + -------- 2 4 4 2
$${{{\rm asinh}\; 6+6\,\sqrt{37}}\over{4}}+{{{\rm asinh}\; 2+2\,
\sqrt{5}}\over{4}}$$
=
=
___ ____ \/ 5 asinh(2) asinh(6) 3*\/ 37 ----- + -------- + -------- + -------- 2 4 4 2
$$\frac{\operatorname{asinh}{\left(2 \right)}}{4} + \frac{\operatorname{asinh}{\left(6 \right)}}{4} + \frac{\sqrt{5}}{2} + \frac{3 \sqrt{37}}{2}$$
The graph
Use the examples entering the upper and lower limits of integration.