def replacement1894(u, v, x):
a = D(u, x)
b = D(v, x)
return Simp(
S(2) * ArcTan(sqrt(u) * Rt(-a * b, S(2)) / (a * sqrt(v))) /
Rt(-a * b, S(2)), x)
def replacement1893(u, v, x):
a = D(u, x)
b = D(v, x)
return Simp(
S(2) * atanh(sqrt(u) * Rt(a * b, S(2)) / (a * sqrt(v))) /
Rt(a * b, S(2)), x)
def replacement1890(u, v, x):
a = D(u, x)
b = D(v, x)
return Simp(
-S(2) * atanh(sqrt(v) / Rt(-(-a * v + b * u) / a, S(2))) /
(a * Rt(-(-a * v + b * u) / a, S(2))), x)
def replacement1889(u, v, x):
a = D(u, x)
b = D(v, x)
return Simp(
S(2) * ArcTan(sqrt(v) / Rt((-a * v + b * u) / a, S(2))) / (a * Rt(
(-a * v + b * u) / a, S(2))), x)
def replacement1891(v, x, u):
a = D(u, x)
b = D(v, x)
rubi.append(1891)
return Simp(
S(2) * ArcTan(sqrt(u) * Rt(-a * b, S(2)) / (a * sqrt(v))) /
Rt(-a * b, S(2)), x)
def replacement1890(v, x, u):
a = D(u, x)
b = D(v, x)
rubi.append(1890)
return Simp(
S(2) * atanh(sqrt(u) * Rt(a * b, S(2)) / (a * sqrt(v))) /
Rt(a * b, S(2)), x)
def replacement1887(v, x, u):
a = D(u, x)
b = D(v, x)
rubi.append(1887)
return Simp(
-S(2) * atanh(sqrt(v) / Rt(-(-a * v + b * u) / a, S(2))) /
(a * Rt(-(-a * v + b * u) / a, S(2))), x)
def replacement1886(v, x, u):
a = D(u, x)
b = D(v, x)
rubi.append(1886)
return Simp(
S(2) * ArcTan(sqrt(v) / Rt((-a * v + b * u) / a, S(2))) / (a * Rt(
(-a * v + b * u) / a, S(2))), x)
def With10(x, v, u):
a = D(u, x)
b = D(v, x)
return S(2) * ArcTan(sqrt(u) * Rt(-a * b, S(2)) /
(a * sqrt(v))) / Rt(-a * b, S(2))
def With9(x, v, u):
a = D(u, x)
b = D(v, x)
return S(2) * atanh(sqrt(u) * Rt(a * b, S(2)) /
(a * sqrt(v))) / Rt(a * b, S(2))
def With6(x, v, u):
a = D(u, x)
b = D(v, x)
return -S(2) * atanh(sqrt(v) / Rt(
(a * v - b * u) / a, S(2))) / (a * Rt((a * v - b * u) / a, S(2)))
def With5(x, v, u):
a = D(u, x)
b = D(v, x)
return S(2) * ArcTan(sqrt(v) / Rt(
(-a * v + b * u) / a, S(2))) / (a * Rt((-a * v + b * u) / a, S(2)))