Simplificación general
[src]
/ ___ \
|\/ 3 *(-1 + 2*x)|
____________ asinh|----------------| / ___ \
/ 2 \ 3 / |\/ 3 *(-2 + x)|
\/ 1 + x - x - ----------------------- + asinh|--------------|
2 \ 3*|x| /
$$\sqrt{x^{2} - x + 1} - \frac{\operatorname{asinh}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)}}{2} + \operatorname{asinh}{\left(\frac{\sqrt{3} \left(x - 2\right)}{3 \left|{x}\right|} \right)}$$
sqrt(1 + x^2 - x) - asinh(sqrt(3)*(-1 + 2*x)/3)/2 + asinh(sqrt(3)*(-2 + x)/(3*|x|))
(1.0 + x^2 - x)^0.5 - 0.5*asinh((2*x - 1)/sqrt(3)) + asinh(x/((sqrt(3)*|x|)) - 2*sqrt(3)/(3*|x|))
(1.0 + x^2 - x)^0.5 - 0.5*asinh((2*x - 1)/sqrt(3)) + asinh(x/((sqrt(3)*|x|)) - 2*sqrt(3)/(3*|x|))
Denominador racional
[src]
/ ___ ___\ ____________ / ___ ___\
| \/ 3 2*x*\/ 3 | / 2 | 2*\/ 3 x*\/ 3 |
- asinh|- ----- + ---------| + 2*\/ 1 + x - x + 2*asinh|- ------- + -------|
\ 3 3 / \ 3*|x| 3*|x| /
-------------------------------------------------------------------------------
2
$$\frac{2 \sqrt{x^{2} - x + 1} - \operatorname{asinh}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)} + 2 \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} - \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}}{2}$$
(-asinh(-sqrt(3)/3 + 2*x*sqrt(3)/3) + 2*sqrt(1 + x^2 - x) + 2*asinh(-2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|)))/2
Abrimos la expresión
[src]
/2*x - 1\
asinh|-------|
____________ | ___ | / ___ ___\
/ 2 \ \/ 3 / | 2*\/ 3 x*\/ 3 |
\/ x - x + 1 - -------------- + asinh|- ------- + -------|
2 \ 3*|x| 3*|x| /
$$\sqrt{\left(x^{2} - x\right) + 1} - \frac{\operatorname{asinh}{\left(\frac{2 x - 1}{\sqrt{3}} \right)}}{2} + \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} - \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}$$
sqrt(x^2 - x + 1) - asinh((2*x - 1)/sqrt(3))/2 + asinh(-2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|))
Compilar la expresión
[src]
/2*x - 1\
asinh|-------|
____________ | ___ |
/ 2 \ \/ 3 / / x 2 \
\/ 1 + x - x - -------------- + asinh|--------- - ---------|
2 | ___ ___ |
\\/ 3 *|x| \/ 3 *|x|/
$$\sqrt{x^{2} - x + 1} - \frac{\operatorname{asinh}{\left(\frac{2 x - 1}{\sqrt{3}} \right)}}{2} + \operatorname{asinh}{\left(\frac{x}{\sqrt{3} \left|{x}\right|} - \frac{2}{\sqrt{3} \left|{x}\right|} \right)}$$
sqrt(1 + x^2 - x) - asinh((2*x - 1)/sqrt(3))/2 + asinh(x/((sqrt(3)*|x|)) - 2*sqrt(3)/(3*|x|))
Parte trigonométrica
[src]
/ ___ \
|\/ 3 *(-1 + 2*x)|
____________ asinh|----------------| / ___ ___\
/ 2 \ 3 / | 2*\/ 3 x*\/ 3 |
\/ 1 + x - x - ----------------------- + asinh|- ------- + -------|
2 \ 3*|x| 3*|x| /
$$\sqrt{x^{2} - x + 1} - \frac{\operatorname{asinh}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)}}{2} + \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} - \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}$$
sqrt(1 + x^2 - x) - asinh(sqrt(3)*(-1 + 2*x)/3)/2 + asinh(-2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|))
Unión de expresiones racionales
[src]
/ ___ \ / ___ \
|\/ 3 *(-1 + 2*x)| ________________ |\/ 3 *(-2 + x)|
- asinh|----------------| + 2*\/ 1 + x*(-1 + x) + 2*asinh|--------------|
\ 3 / \ 3*|x| /
--------------------------------------------------------------------------
2
$$\frac{2 \sqrt{x \left(x - 1\right) + 1} - \operatorname{asinh}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)} + 2 \operatorname{asinh}{\left(\frac{\sqrt{3} \left(x - 2\right)}{3 \left|{x}\right|} \right)}}{2}$$
(-asinh(sqrt(3)*(-1 + 2*x)/3) + 2*sqrt(1 + x*(-1 + x)) + 2*asinh(sqrt(3)*(-2 + x)/(3*|x|)))/2
/ ___ / 1 2*x\\
____________ asinh|\/ 3 *|- - + ---|| / ___ ___\
/ 2 \ \ 3 3 // | 2*\/ 3 x*\/ 3 |
\/ 1 + x - x - ------------------------ + asinh|- ------- + -------|
2 \ 3*|x| 3*|x| /
$$\sqrt{x^{2} - x + 1} - \frac{\operatorname{asinh}{\left(\sqrt{3} \left(\frac{2 x}{3} - \frac{1}{3}\right) \right)}}{2} + \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} - \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}$$
/ ___ \
|\/ 3 *(-1 + 2*x)|
____________ asinh|----------------| / ___ ___\
/ 2 \ 3 / | 2*\/ 3 x*\/ 3 |
\/ 1 + x - x - ----------------------- + asinh|- ------- + -------|
2 \ 3*|x| 3*|x| /
$$\sqrt{x^{2} - x + 1} - \frac{\operatorname{asinh}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)}}{2} + \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} - \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}$$
sqrt(1 + x^2 - x) - asinh(sqrt(3)*(-1 + 2*x)/3)/2 + asinh(-2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|))
/ ___ ___\
| \/ 3 2*x*\/ 3 |
____________ asinh|- ----- + ---------| / ___ ___\
/ 2 \ 3 3 / | 2*\/ 3 x*\/ 3 |
\/ 1 + x - x - -------------------------- + asinh|- ------- + -------|
2 \ 3*|x| 3*|x| /
$$\sqrt{x^{2} - x + 1} - \frac{\operatorname{asinh}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{2} + \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} - \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}$$
sqrt(1 + x^2 - x) - asinh(-sqrt(3)/3 + 2*x*sqrt(3)/3)/2 + asinh(-2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|))
/ ___ ___\
| \/ 3 2*x*\/ 3 |
____________ asinh|- ----- + ---------| / ___ ___\
/ 2 \ 3 3 / | 2*\/ 3 x*\/ 3 |
\/ 1 + x - x - -------------------------- + asinh|- ------- + -------|
2 \ 3*|x| 3*|x| /
$$\sqrt{x^{2} - x + 1} - \frac{\operatorname{asinh}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{2} + \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} - \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}$$
sqrt(1 + x^2 - x) - asinh(-sqrt(3)/3 + 2*x*sqrt(3)/3)/2 + asinh(-2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|))