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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of 1/(lnx)
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Integral of x^2/(1+x^2)^2
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Integral of e^(2x+3)
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Integral of dx/(2+x^2)
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Identical expressions
- sqrt(one -x^ two)+sqrt(eighteen -x^ two)- three *sqrt(two)
- square root of (1 minus x squared ) plus square root of (18 minus x squared ) minus 3 multiply by square root of (2)
- square root of (one minus x to the power of two) plus square root of (eighteen minus x to the power of two) minus three multiply by square root of (two)
- √(1-x^2)+√(18-x^2)-3*√(2)
- sqrt(1-x2)+sqrt(18-x2)-3*sqrt(2)
- sqrt1-x2+sqrt18-x2-3*sqrt2
- sqrt(1-x²)+sqrt(18-x²)-3*sqrt(2)
- sqrt(1-x to the power of 2)+sqrt(18-x to the power of 2)-3*sqrt(2)
- sqrt(1-x^2)+sqrt(18-x^2)-3sqrt(2)
- sqrt(1-x2)+sqrt(18-x2)-3sqrt(2)
- sqrt1-x2+sqrt18-x2-3sqrt2
- sqrt1-x^2+sqrt18-x^2-3sqrt2
- sqrt(1-x^2)+sqrt(18-x^2)-3*sqrt(2)dx
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Similar expressions
- sqrt(1-x^2)+sqrt(18-x^2)+3*sqrt(2)
- sqrt(1-x^2)+sqrt(18+x^2)-3*sqrt(2)
- sqrt(1-x^2)-sqrt(18-x^2)-3*sqrt(2)
- sqrt(1+x^2)+sqrt(18-x^2)-3*sqrt(2)
Integral of sqrt(1-x^2)+sqrt(18-x^2)-3*sqrt(2) dx
The solution
You have entered
[src]
_____
\/ 142
-------
12
/
|
| / ________ _________ \
| | / 2 / 2 ___|
| \\/ 1 - x + \/ 18 - x - 3*\/ 2 / dx
|
/
0
$$\int\limits_{0}^{\frac{\sqrt{142}}{12}} \left(\sqrt{1 - x^{2}} + \sqrt{18 - x^{2}} - 3 \sqrt{2}\right)\, dx$$
Integral(sqrt(1 - x^2) + sqrt(18 - x^2) - 3*sqrt(2), (x, 0, sqrt(142)/12))
Detail solution
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Integrate term-by-term:
SqrtQuadraticRule(a=1, b=0, c=-1, context=sqrt(1 - x**2), symbol=x)
SqrtQuadraticRule(a=18, b=0, c=-1, context=sqrt(18 - x**2), symbol=x)
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The integral of a constant is the constant times the variable of integration:
The result is:
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Add the constant of integration:
The answer is:
The answer (Indefinite)
[src]
/ | ________ _________ | / ________ _________ \ / ___\ / 2 / 2 | | / 2 / 2 ___| asin(x) |x*\/ 2 | x*\/ 1 - x x*\/ 18 - x ___ | \\/ 1 - x + \/ 18 - x - 3*\/ 2 / dx = C + ------- + 9*asin|-------| + ------------- + -------------- - 3*x*\/ 2 | 2 \ 6 / 2 2 /
$$\int \left(\sqrt{1 - x^{2}} + \sqrt{18 - x^{2}} - 3 \sqrt{2}\right)\, dx = C + \frac{x \sqrt{1 - x^{2}}}{2} + \frac{x \sqrt{18 - x^{2}}}{2} - 3 \sqrt{2} x + \frac{\operatorname{asin}{\left(x \right)}}{2} + 9 \operatorname{asin}{\left(\frac{\sqrt{2} x}{6} \right)}$$
The graph
The answer
[src]
/ _____\
|\/ 142 |
asin|-------| / ____\ ____
\ 12 / |\/ 71 | \/ 71
------------- + 9*asin|------| - ------
2 \ 36 / 4
$$- \frac{\sqrt{71}}{4} + \frac{\operatorname{asin}{\left(\frac{\sqrt{142}}{12} \right)}}{2} + 9 \operatorname{asin}{\left(\frac{\sqrt{71}}{36} \right)}$$
=
=
/ _____\
|\/ 142 |
asin|-------| / ____\ ____
\ 12 / |\/ 71 | \/ 71
------------- + 9*asin|------| - ------
2 \ 36 / 4
$$- \frac{\sqrt{71}}{4} + \frac{\operatorname{asin}{\left(\frac{\sqrt{142}}{12} \right)}}{2} + 9 \operatorname{asin}{\left(\frac{\sqrt{71}}{36} \right)}$$
The graph
Use the examples entering the upper and lower limits of integration.