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- Improper integral
- Double Integral
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How to use it?
- Integral of d{x}:
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Integral of exp(y)
- Integral of log(x)^3/x
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Integral of x^2*e^(x^3)*dx
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Integral of 1÷(x^2-1)
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Identical expressions
- sqrt((4x+ one)/(4x))
- square root of ((4x plus 1) divide by (4x))
- square root of ((4x plus one) divide by (4x))
- √((4x+1)/(4x))
- sqrt4x+1/4x
- sqrt((4x+1) divide by (4x))
- sqrt((4x+1)/(4x))dx
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Similar expressions
- sqrt((4x-1)/(4x))
Integral of sqrt((4x+1)/(4x)) dx
The solution
You have entered
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1 / | | _________ | / 4*x + 1 | / ------- dx | \/ 4*x | / 0
$$\int\limits_{0}^{1} \sqrt{\frac{4 x + 1}{4 x}}\, dx$$
Integral(sqrt((4*x + 1)/((4*x))), (x, 0, 1))
The answer (Indefinite)
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/ | | _________ / ___\ ___ _________ | / 4*x + 1 asinh\2*\/ x / \/ x *\/ 1 + 4*x | / ------- dx = C + -------------- + ----------------- | \/ 4*x 4 2 | /
$$\int \sqrt{\frac{4 x + 1}{4 x}}\, dx = C + \frac{\sqrt{x} \sqrt{4 x + 1}}{2} + \frac{\operatorname{asinh}{\left(2 \sqrt{x} \right)}}{4}$$
The answer
[src]
___ / ___\ \/ 5 acosh\\/ 5 / ----- + ------------ 2 4
$$\frac{\operatorname{acosh}{\left(\sqrt{5} \right)}}{4} + \frac{\sqrt{5}}{2}$$
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___ / ___\ \/ 5 acosh\\/ 5 / ----- + ------------ 2 4
$$\frac{\operatorname{acosh}{\left(\sqrt{5} \right)}}{4} + \frac{\sqrt{5}}{2}$$
sqrt(5)/2 + acosh(sqrt(5))/4
Use the examples entering the upper and lower limits of integration.