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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of x^2/(1+x^3)
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Integral of x^2/sqrt(4-x^2)
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Integral of e^x²
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Integral of x^2+x^3
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Identical expressions
- (sqrt(x)- one)/(sqrt^ three (x)+ one)
- ( square root of (x) minus 1) divide by ( square root of cubed (x) plus 1)
- ( square root of (x) minus one) divide by ( square root of to the power of three (x) plus one)
- (√(x)-1)/(√^3(x)+1)
- (sqrt(x)-1)/(sqrt3(x)+1)
- sqrtx-1/sqrt3x+1
- (sqrt(x)-1)/(sqrt³(x)+1)
- (sqrt(x)-1)/(sqrt to the power of 3(x)+1)
- sqrtx-1/sqrt^3x+1
- (sqrt(x)-1) divide by (sqrt^3(x)+1)
- (sqrt(x)-1)/(sqrt^3(x)+1)dx
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Similar expressions
- (sqrt(x)+1)/(sqrt^3(x)+1)
- (sqrt(x)-1)/(sqrt^3(x)-1)
Integral of (sqrt(x)-1)/(sqrt^3(x)+1) dx
The solution
You have entered
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1 / | | ___ | \/ x - 1 | ---------- dx | 3 | ___ | \/ x + 1 | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x} - 1}{\left(\sqrt{x}\right)^{3} + 1}\, dx$$
Integral((sqrt(x) - 1)/((sqrt(x))^3 + 1), (x, 0, 1))
The answer (Indefinite)
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/ ___ / 1 ___\\ / |2*\/ 3 *|- - + \/ x || | ___ | \ 2 /| | ___ / ___\ / ___\ 2*\/ 3 *atan|---------------------| | \/ x - 1 log\1 + x - \/ x / 4*log\1 + \/ x / \ 3 / | ---------- dx = C + ------------------ + ---------------- - ----------------------------------- | 3 3 3 3 | ___ | \/ x + 1 | /
$$\int \frac{\sqrt{x} - 1}{\left(\sqrt{x}\right)^{3} + 1}\, dx = C + \frac{4 \log{\left(\sqrt{x} + 1 \right)}}{3} + \frac{\log{\left(- \sqrt{x} + x + 1 \right)}}{3} - \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(\sqrt{x} - \frac{1}{2}\right)}{3} \right)}}{3}$$
The graph
The answer
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___ 4*log(2) 2*pi*\/ 3 -------- - ---------- 3 9
$$- \frac{2 \sqrt{3} \pi}{9} + \frac{4 \log{\left(2 \right)}}{3}$$
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___ 4*log(2) 2*pi*\/ 3 -------- - ---------- 3 9
$$- \frac{2 \sqrt{3} \pi}{9} + \frac{4 \log{\left(2 \right)}}{3}$$
4*log(2)/3 - 2*pi*sqrt(3)/9
Use the examples entering the upper and lower limits of integration.