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How to use it?
- Integral of d{x}:
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Integral of x^4/(x^2+1)
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Integral of sqrt(x^2-1)/x
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Integral of dx/((2*x))
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Integral of dx/sinxcosx
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Identical expressions
- sqrt(x)/(nine +4x^ two)
- square root of (x) divide by (9 plus 4x squared )
- square root of (x) divide by (nine plus 4x to the power of two)
- √(x)/(9+4x^2)
- sqrt(x)/(9+4x2)
- sqrtx/9+4x2
- sqrt(x)/(9+4x²)
- sqrt(x)/(9+4x to the power of 2)
- sqrtx/9+4x^2
- sqrt(x) divide by (9+4x^2)
- sqrt(x)/(9+4x^2)dx
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Similar expressions
- sqrt(x)/(9-4x^2)
Integral of sqrt(x)/(9+4x^2) dx
The solution
You have entered
[src]
1 / | | ___ | \/ x | -------- dx | 2 | 9 + 4*x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x}}{4 x^{2} + 9}\, dx$$
Integral(sqrt(x)/(9 + 4*x^2), (x, 0, 1))
The answer (Indefinite)
[src]
/ / ___ ___\ / ___ ___\ | ___ /3 ___ ___\ ___ | 2*\/ 3 *\/ x | ___ | 2*\/ 3 *\/ x | ___ /3 ___ ___\ | ___ \/ 3 *log|- + x + \/ 3 *\/ x | \/ 3 *atan|1 + -------------| \/ 3 *atan|-1 + -------------| \/ 3 *log|- + x - \/ 3 *\/ x | | \/ x \2 / \ 3 / \ 3 / \2 / | -------- dx = C - ------------------------------ + ----------------------------- + ------------------------------ + ------------------------------ | 2 24 12 12 24 | 9 + 4*x | /
$$\int \frac{\sqrt{x}}{4 x^{2} + 9}\, dx = C + \frac{\sqrt{3} \log{\left(- \sqrt{3} \sqrt{x} + x + \frac{3}{2} \right)}}{24} - \frac{\sqrt{3} \log{\left(\sqrt{3} \sqrt{x} + x + \frac{3}{2} \right)}}{24} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \sqrt{x}}{3} - 1 \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \sqrt{x}}{3} + 1 \right)}}{12}$$
The graph
The answer
[src]
/ ___\ / ___\
___ | 2*\/ 3 | ___ | 2*\/ 3 |
\/ 3 *atan|1 - -------| ___ / ___\ \/ 3 *atan|1 + -------| ___ / ___\
\ 3 / \/ 3 *log\10 + 4*\/ 3 / \ 3 / \/ 3 *log\10 - 4*\/ 3 /
- ----------------------- - ----------------------- + ----------------------- + -----------------------
12 24 12 24
$$- \frac{\sqrt{3} \log{\left(4 \sqrt{3} + 10 \right)}}{24} - \frac{\sqrt{3} \operatorname{atan}{\left(1 - \frac{2 \sqrt{3}}{3} \right)}}{12} + \frac{\sqrt{3} \log{\left(10 - 4 \sqrt{3} \right)}}{24} + \frac{\sqrt{3} \operatorname{atan}{\left(1 + \frac{2 \sqrt{3}}{3} \right)}}{12}$$
=
=
/ ___\ / ___\
___ | 2*\/ 3 | ___ | 2*\/ 3 |
\/ 3 *atan|1 - -------| ___ / ___\ \/ 3 *atan|1 + -------| ___ / ___\
\ 3 / \/ 3 *log\10 + 4*\/ 3 / \ 3 / \/ 3 *log\10 - 4*\/ 3 /
- ----------------------- - ----------------------- + ----------------------- + -----------------------
12 24 12 24
$$- \frac{\sqrt{3} \log{\left(4 \sqrt{3} + 10 \right)}}{24} - \frac{\sqrt{3} \operatorname{atan}{\left(1 - \frac{2 \sqrt{3}}{3} \right)}}{12} + \frac{\sqrt{3} \log{\left(10 - 4 \sqrt{3} \right)}}{24} + \frac{\sqrt{3} \operatorname{atan}{\left(1 + \frac{2 \sqrt{3}}{3} \right)}}{12}$$
-sqrt(3)*atan(1 - 2*sqrt(3)/3)/12 - sqrt(3)*log(10 + 4*sqrt(3))/24 + sqrt(3)*atan(1 + 2*sqrt(3)/3)/12 + sqrt(3)*log(10 - 4*sqrt(3))/24
Use the examples entering the upper and lower limits of integration.