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How to use it?
- Integral of d{x}:
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Integral of sin(5x)
- Integral of dx/x*lnx
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Integral of e^x/sqrt(e^(2*x)-1)
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Integral of e^(-x)/sqrt(x)
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Identical expressions
- (x+ twenty)/(x^ three - eight)
- (x plus 20) divide by (x cubed minus 8)
- (x plus twenty) divide by (x to the power of three minus eight)
- (x+20)/(x3-8)
- x+20/x3-8
- (x+20)/(x³-8)
- (x+20)/(x to the power of 3-8)
- x+20/x^3-8
- (x+20) divide by (x^3-8)
- (x+20)/(x^3-8)dx
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Similar expressions
- (x-20)/(x^3-8)
- (x+20)/(x^3+8)
Integral of (x+20)/(x^3-8) dx
The solution
You have entered
[src]
1 / | | x + 20 | ------ dx | 3 | x - 8 | / 0
$$\int\limits_{0}^{1} \frac{x + 20}{x^{3} - 8}\, dx$$
Integral((x + 20)/(x^3 - 8), (x, 0, 1))
The answer (Indefinite)
[src]
/ ___ \ / ___ |\/ 3 *(1 + x)| | / 2 \ 3*\/ 3 *atan|-------------| | x + 20 11*log\4 + x + 2*x/ 11*log(-2 + x) \ 3 / | ------ dx = C - -------------------- + -------------- - --------------------------- | 3 12 6 2 | x - 8 | /
$$\int \frac{x + 20}{x^{3} - 8}\, dx = C + \frac{11 \log{\left(x - 2 \right)}}{6} - \frac{11 \log{\left(x^{2} + 2 x + 4 \right)}}{12} - \frac{3 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x + 1\right)}{3} \right)}}{2}$$
The graph
The answer
[src]
/ ___\
___ |2*\/ 3 |
3*\/ 3 *atan|-------| ___
11*log(2) 11*log(7) 11*log(4) \ 3 / pi*\/ 3
- --------- - --------- + --------- - --------------------- + --------
6 12 12 2 4
$$- \frac{3 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{2} - \frac{11 \log{\left(7 \right)}}{12} - \frac{11 \log{\left(2 \right)}}{6} + \frac{11 \log{\left(4 \right)}}{12} + \frac{\sqrt{3} \pi}{4}$$
=
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/ ___\
___ |2*\/ 3 |
3*\/ 3 *atan|-------| ___
11*log(2) 11*log(7) 11*log(4) \ 3 / pi*\/ 3
- --------- - --------- + --------- - --------------------- + --------
6 12 12 2 4
$$- \frac{3 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{2} - \frac{11 \log{\left(7 \right)}}{12} - \frac{11 \log{\left(2 \right)}}{6} + \frac{11 \log{\left(4 \right)}}{12} + \frac{\sqrt{3} \pi}{4}$$
-11*log(2)/6 - 11*log(7)/12 + 11*log(4)/12 - 3*sqrt(3)*atan(2*sqrt(3)/3)/2 + pi*sqrt(3)/4
The graph
Use the examples entering the upper and lower limits of integration.