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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x/(3x²-1)^4
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Integral of x^(4/5)
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Integral of (x^2)sinx
- Integral of tan(x*d)^3*tan(x)
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Identical expressions
- one /(sqrt(x+ one)+sqrt(x))
- 1 divide by ( square root of (x plus 1) plus square root of (x))
- one divide by ( square root of (x plus one) plus square root of (x))
- 1/(√(x+1)+√(x))
- 1/sqrtx+1+sqrtx
- 1 divide by (sqrt(x+1)+sqrt(x))
- 1/(sqrt(x+1)+sqrt(x))dx
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Similar expressions
- 1/(sqrt(x-1)+sqrt(x))
- 1/(sqrt(x+1)-sqrt(x))
- 1/(sqrt(x+1)+sqrt((x+1)^(3)))
- 1/(sqrt(x+1)+sqrt(x+1)^3)
- 1/(sqrt(x+1)+sqrt(x-1))
Integral of 1/(sqrt(x+1)+sqrt(x)) dx
The solution
You have entered
[src]
1 / | | 1 | 1*----------------- dx | _______ ___ | \/ x + 1 + \/ x | / 0
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{\sqrt{x} + \sqrt{x + 1}}\, dx$$
Integral(1/(sqrt(x + 1) + sqrt(x)), (x, 0, 1))
The answer (Indefinite)
[src]
// ___ 3/2 ___ \ / || 2*\/ x 2*(1 + x) 2*\/ x *(1 + x) | | || ------- + ------------ - --------------- for |1 + x| > 1| | 1 || 3 3 3 | | 1*----------------- dx = C + |< | | _______ ___ || 3/2 ____ ____ | | \/ x + 1 + \/ x ||2*(1 + x) 2*I*\/ -x 2*I*\/ -x *(1 + x) | | ||------------ + ---------- - ------------------ otherwise | / \\ 3 3 3 /
$$\int {{{1}\over{\sqrt{x+1}+\sqrt{x}}}}{\;dx}$$
The graph
The answer
[src]
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2 6 2*\/ 2
- - + ----------- + -----------
3 ___ ___
3 + 3*\/ 2 3 + 3*\/ 2
$$\int_{0}^{1}{{{1}\over{\sqrt{x+1}+\sqrt{x}}}\;dx}$$
=
=
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2 6 2*\/ 2
- - + ----------- + -----------
3 ___ ___
3 + 3*\/ 2 3 + 3*\/ 2
$$- \frac{2}{3} + \frac{2 \sqrt{2}}{3 + 3 \sqrt{2}} + \frac{6}{3 + 3 \sqrt{2}}$$
The graph
Use the examples entering the upper and lower limits of integration.