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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of dx/(1-4*x^2)
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Integral of dx/sin^2x
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Integral of (2x+3)
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Integral of (3-x^2)^3
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Identical expressions
- x/(four ^sqrt(4x+ one))
- x divide by (4 to the power of square root of (4x plus 1))
- x divide by (four to the power of square root of (4x plus one))
- x/(4^√(4x+1))
- x/(4sqrt(4x+1))
- x/4sqrt4x+1
- x/4^sqrt4x+1
- x divide by (4^sqrt(4x+1))
- x/(4^sqrt(4x+1))dx
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Similar expressions
- x/(4^sqrt(4x-1))
Integral of x/(4^sqrt(4x+1)) dx
The solution
You have entered
[src]
1 / | | x | ------------ dx | _________ | \/ 4*x + 1 | 4 | / 0
$$\int\limits_{0}^{1} \frac{x}{4^{\sqrt{4 x + 1}}}\, dx$$
Integral(x/4^(sqrt(4*x + 1)), (x, 0, 1))
The answer (Indefinite)
[src]
/ / | | | _________ | x | -\/ 4*x + 1 | ------------ dx = C + | x*4 dx | _________ | | \/ 4*x + 1 / | 4 | /
$$\int \frac{x}{4^{\sqrt{4 x + 1}}}\, dx = C + \int 4^{- \sqrt{4 x + 1}} x\, dx$$
The graph
The answer
[src]
___ ___ ___ ___
-\/ 5 -\/ 5 -\/ 5 ___ -\/ 5 ___
1 3 3 7*4 3*4 3*4 *\/ 5 4 *\/ 5
---------- + ----------- + ----------- - ---------- - ---------- - --------------- - -------------
2 3 4 2 4 3 4*log(2)
64*log (2) 128*log (2) 256*log (2) 16*log (2) 64*log (2) 32*log (2)
$$- \frac{7}{16 \cdot 4^{\sqrt{5}} \log{\left(2 \right)}^{2}} - \frac{\sqrt{5}}{4 \cdot 4^{\sqrt{5}} \log{\left(2 \right)}} - \frac{3 \sqrt{5}}{32 \cdot 4^{\sqrt{5}} \log{\left(2 \right)}^{3}} - \frac{3}{64 \cdot 4^{\sqrt{5}} \log{\left(2 \right)}^{4}} + \frac{1}{64 \log{\left(2 \right)}^{2}} + \frac{3}{256 \log{\left(2 \right)}^{4}} + \frac{3}{128 \log{\left(2 \right)}^{3}}$$
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___ ___ ___ ___
-\/ 5 -\/ 5 -\/ 5 ___ -\/ 5 ___
1 3 3 7*4 3*4 3*4 *\/ 5 4 *\/ 5
---------- + ----------- + ----------- - ---------- - ---------- - --------------- - -------------
2 3 4 2 4 3 4*log(2)
64*log (2) 128*log (2) 256*log (2) 16*log (2) 64*log (2) 32*log (2)
$$- \frac{7}{16 \cdot 4^{\sqrt{5}} \log{\left(2 \right)}^{2}} - \frac{\sqrt{5}}{4 \cdot 4^{\sqrt{5}} \log{\left(2 \right)}} - \frac{3 \sqrt{5}}{32 \cdot 4^{\sqrt{5}} \log{\left(2 \right)}^{3}} - \frac{3}{64 \cdot 4^{\sqrt{5}} \log{\left(2 \right)}^{4}} + \frac{1}{64 \log{\left(2 \right)}^{2}} + \frac{3}{256 \log{\left(2 \right)}^{4}} + \frac{3}{128 \log{\left(2 \right)}^{3}}$$
1/(64*log(2)^2) + 3/(128*log(2)^3) + 3/(256*log(2)^4) - 7*4^(-sqrt(5))/(16*log(2)^2) - 3*4^(-sqrt(5))/(64*log(2)^4) - 3*4^(-sqrt(5))*sqrt(5)/(32*log(2)^3) - 4^(-sqrt(5))*sqrt(5)/(4*log(2))
Use the examples entering the upper and lower limits of integration.