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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^(1/3)
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Integral of sin(x)^4
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Integral of cos(x)^3
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Integral of (e^(x^2))
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Identical expressions
- one /(9x- four)*sqrtx
- 1 divide by (9x minus 4) multiply by square root of x
- one divide by (9x minus four) multiply by square root of x
- 1/(9x-4)*√x
- 1/(9x-4)sqrtx
- 1/9x-4sqrtx
- 1 divide by (9x-4)*sqrtx
- 1/(9x-4)*sqrtxdx
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Similar expressions
- 1/(9x+4)*sqrtx
Integral of 1/(9x-4)*sqrtx dx
The solution
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[src]
4 / | | ___ | \/ x | ------- dx | 9*x - 4 | / 1
$$\int\limits_{1}^{4} \frac{\sqrt{x}}{9 x - 4}\, dx$$
Integral(sqrt(x)/(9*x - 4), (x, 1, 4))
The answer (Indefinite)
[src]
/ | | ___ / ___\ ___ / ___\ | \/ x 2*log\2 + 3*\/ x / 2*\/ x 2*log\-2 + 3*\/ x / | ------- dx = C - ------------------ + ------- + ------------------- | 9*x - 4 27 9 27 | /
$$\int \frac{\sqrt{x}}{9 x - 4}\, dx = C + \frac{2 \sqrt{x}}{9} + \frac{2 \log{\left(3 \sqrt{x} - 2 \right)}}{27} - \frac{2 \log{\left(3 \sqrt{x} + 2 \right)}}{27}$$
The graph
The answer
[src]
2 2*log(8/3) 2*log(3) 2*log(4/3) 2*log(5/3) - - ---------- + -------- + ---------- + ---------- 9 27 27 27 27
$$- \frac{2 \log{\left(\frac{8}{3} \right)}}{27} + \frac{2 \log{\left(\frac{4}{3} \right)}}{27} + \frac{2 \log{\left(\frac{5}{3} \right)}}{27} + \frac{2 \log{\left(3 \right)}}{27} + \frac{2}{9}$$
=
=
2 2*log(8/3) 2*log(3) 2*log(4/3) 2*log(5/3) - - ---------- + -------- + ---------- + ---------- 9 27 27 27 27
$$- \frac{2 \log{\left(\frac{8}{3} \right)}}{27} + \frac{2 \log{\left(\frac{4}{3} \right)}}{27} + \frac{2 \log{\left(\frac{5}{3} \right)}}{27} + \frac{2 \log{\left(3 \right)}}{27} + \frac{2}{9}$$
2/9 - 2*log(8/3)/27 + 2*log(3)/27 + 2*log(4/3)/27 + 2*log(5/3)/27
Use the examples entering the upper and lower limits of integration.