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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of e^(x^2)
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Integral of sin(x)^3
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Integral of √(x^2+1)
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Integral of cos(5x)
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Identical expressions
- one /(one +sqrt(x+ one)^ three)
- 1 divide by (1 plus square root of (x plus 1) cubed )
- one divide by (one plus square root of (x plus one) to the power of three)
- 1/(1+√(x+1)^3)
- 1/(1+sqrt(x+1)3)
- 1/1+sqrtx+13
- 1/(1+sqrt(x+1)³)
- 1/(1+sqrt(x+1) to the power of 3)
- 1/1+sqrtx+1^3
- 1 divide by (1+sqrt(x+1)^3)
- 1/(1+sqrt(x+1)^3)dx
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Similar expressions
- 1/(1+sqrt(x-1)^3)
- 1/(1-sqrt(x+1)^3)
Integral of 1/(1+sqrt(x+1)^3) dx
The solution
You have entered
[src]
1 / | | 1 | -------------- dx | 3 | _______ | 1 + \/ x + 1 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(\sqrt{x + 1}\right)^{3} + 1}\, dx$$
Integral(1/(1 + (sqrt(x + 1))^3), (x, 0, 1))
The answer (Indefinite)
[src]
/ ___ / 1 _______\\
|2*\/ 3 *|- - + \/ x + 1 ||
/ ___ | \ 2 /|
| / _______\ / _______\ 2*\/ 3 *atan|-------------------------|
| 1 2*log\1 + \/ x + 1 / log\2 + x - \/ x + 1 / \ 3 /
| -------------- dx = C - -------------------- + ---------------------- + ---------------------------------------
| 3 3 3 3
| _______
| 1 + \/ x + 1
|
/
$$\int \frac{1}{\left(\sqrt{x + 1}\right)^{3} + 1}\, dx = C - \frac{2 \log{\left(\sqrt{x + 1} + 1 \right)}}{3} + \frac{\log{\left(x - \sqrt{x + 1} + 2 \right)}}{3} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(\sqrt{x + 1} - \frac{1}{2}\right)}{3} \right)}}{3}$$
The graph
The answer
[src]
/ ___ ___\
___ | 2*\/ 6 \/ 3 |
/ ___\ / ___\ 2*\/ 3 *atan|- ------- + -----| ___
2*log\1 + \/ 2 / log(4) log\12 - 4*\/ 2 / 2*log(2) \ 3 3 / pi*\/ 3
- ---------------- - ------ + ----------------- + -------- - ------------------------------- - --------
3 3 3 3 3 9
$$- \frac{\sqrt{3} \pi}{9} - \frac{2 \log{\left(1 + \sqrt{2} \right)}}{3} - \frac{\log{\left(4 \right)}}{3} + \frac{2 \log{\left(2 \right)}}{3} + \frac{\log{\left(12 - 4 \sqrt{2} \right)}}{3} - \frac{2 \sqrt{3} \operatorname{atan}{\left(- \frac{2 \sqrt{6}}{3} + \frac{\sqrt{3}}{3} \right)}}{3}$$
=
=
/ ___ ___\
___ | 2*\/ 6 \/ 3 |
/ ___\ / ___\ 2*\/ 3 *atan|- ------- + -----| ___
2*log\1 + \/ 2 / log(4) log\12 - 4*\/ 2 / 2*log(2) \ 3 3 / pi*\/ 3
- ---------------- - ------ + ----------------- + -------- - ------------------------------- - --------
3 3 3 3 3 9
$$- \frac{\sqrt{3} \pi}{9} - \frac{2 \log{\left(1 + \sqrt{2} \right)}}{3} - \frac{\log{\left(4 \right)}}{3} + \frac{2 \log{\left(2 \right)}}{3} + \frac{\log{\left(12 - 4 \sqrt{2} \right)}}{3} - \frac{2 \sqrt{3} \operatorname{atan}{\left(- \frac{2 \sqrt{6}}{3} + \frac{\sqrt{3}}{3} \right)}}{3}$$
-2*log(1 + sqrt(2))/3 - log(4)/3 + log(12 - 4*sqrt(2))/3 + 2*log(2)/3 - 2*sqrt(3)*atan(-2*sqrt(6)/3 + sqrt(3)/3)/3 - pi*sqrt(3)/9
Use the examples entering the upper and lower limits of integration.