Integral de (x^2-a)^1/2dx dx
Solución
Respuesta (Indefinida)
[src]
// / x \ \
|| a*acosh|-----| |
|| | ___| 3 ___ | 2| |
|| \\/ a / x x*\/ a |x | |
||- -------------- + ---------------------- - ---------------- for |--| > 1|
/ || 2 _________ _________ |a | |
| || / 2 / 2 |
| ________ || ___ / x / x |
| / 2 || 2*\/ a * / -1 + -- 2* / -1 + -- |
| \/ x - a dx = C + |< \/ a \/ a |
| || |
/ || ________ |
|| / x \ / 2 |
|| I*a*asin|-----| ___ / x |
|| | ___| I*x*\/ a * / 1 - -- |
|| \\/ a / \/ a |
|| --------------- + ----------------------- otherwise |
|| 2 2 |
\\ /
∫−a+x2dx=C+⎩⎨⎧−2−1+ax2ax−2aacosh(ax)+2a−1+ax2x32iax1−ax2+2iaasin(ax)forax2>1otherwise
1
/
|
| / ___ 2 4 2 2
| | \/ a x x 3*x x
| |- -------------- + -------------------- - ------------------- + ---------------------- for --- > 1
| | _________ 3/2 3/2 _________ |a|
| | / 2 / 2\ / 2\ / 2
| | / x ___ | x | 3/2 | x | ___ / x
| | / -1 + -- 2*\/ a *|-1 + --| 2*a *|-1 + --| 2*\/ a * / -1 + --
| | \/ a \ a / \ a / \/ a
| |
| | ________
| < / 2 dx
| | ___ / x
| | I*\/ a * / 1 - -- ___ 2
| | \/ a I*\/ a I*x
| | --------------------- + --------------- - --------------------- otherwise
| | 2 ________ ________
| | / 2 / 2
| | / x ___ / x
| | 2* / 1 - -- 2*\/ a * / 1 - --
| | \/ a \/ a
| \
|
/
0
0∫1⎩⎨⎧−−1+ax2a+2a−1+ax23x2+2a(−1+ax2)23x2−2a23(−1+ax2)23x42ia1−ax2+21−ax2ia−2a1−ax2ix2for∣a∣x2>1otherwisedx
=
1
/
|
| / ___ 2 4 2 2
| | \/ a x x 3*x x
| |- -------------- + -------------------- - ------------------- + ---------------------- for --- > 1
| | _________ 3/2 3/2 _________ |a|
| | / 2 / 2\ / 2\ / 2
| | / x ___ | x | 3/2 | x | ___ / x
| | / -1 + -- 2*\/ a *|-1 + --| 2*a *|-1 + --| 2*\/ a * / -1 + --
| | \/ a \ a / \ a / \/ a
| |
| | ________
| < / 2 dx
| | ___ / x
| | I*\/ a * / 1 - -- ___ 2
| | \/ a I*\/ a I*x
| | --------------------- + --------------- - --------------------- otherwise
| | 2 ________ ________
| | / 2 / 2
| | / x ___ / x
| | 2* / 1 - -- 2*\/ a * / 1 - --
| | \/ a \/ a
| \
|
/
0
0∫1⎩⎨⎧−−1+ax2a+2a−1+ax23x2+2a(−1+ax2)23x2−2a23(−1+ax2)23x42ia1−ax2+21−ax2ia−2a1−ax2ix2for∣a∣x2>1otherwisedx
Integral(Piecewise((-sqrt(a)/sqrt(-1 + x^2/a) + x^2/(2*sqrt(a)*(-1 + x^2/a)^(3/2)) - x^4/(2*a^(3/2)*(-1 + x^2/a)^(3/2)) + 3*x^2/(2*sqrt(a)*sqrt(-1 + x^2/a)), x^2/|a| > 1), (i*sqrt(a)*sqrt(1 - x^2/a)/2 + i*sqrt(a)/(2*sqrt(1 - x^2/a)) - i*x^2/(2*sqrt(a)*sqrt(1 - x^2/a)), True)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.