Hyperbolic sine: Integration (formula 01.19.21.0686)

Sinh

$Mathematica Notation$

Elementary Functions

Sinh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric functions

Involving rational functions of sin

Involving sin(e z) sinh(c z)/a+b sin(d z)

http://functions.wolfram.com/01.19.21.0686.01

Input Form

Integrate[(Sin[e z] Sinh[c z])/(a + b Sin[d z]), z] == I b ((-(E^((-c + I d + I e) z) Hypergeometric2F1[(d + I (c - I e))/d, 1, (2 d + I (c - I e))/d, (b E^(I d z))/((-I) a + Sqrt[-a^2 + b^2])])/ (((-I) a + Sqrt[-a^2 + b^2]) (d + I (c - I e))) - (E^((-c + I d + I e) z) Hypergeometric2F1[(d + I (c - I e))/d, 1, (2 d + I (c - I e))/d, -((b E^(I d z))/(I a + Sqrt[-a^2 + b^2]))])/ ((I a + Sqrt[-a^2 + b^2]) (d + I (c - I e))) + (E^((c + I d + I e) z) Hypergeometric2F1[(d - I (c + I e))/d, 1, (2 d - I (c + I e))/d, (b E^(I d z))/((-I) a + Sqrt[-a^2 + b^2])])/ (((-I) a + Sqrt[-a^2 + b^2]) (d - I (c + I e))) + (E^((c + I d + I e) z) Hypergeometric2F1[(d - I (c + I e))/d, 1, (2 d - I (c + I e))/d, -((b E^(I d z))/(I a + Sqrt[-a^2 + b^2]))])/ ((I a + Sqrt[-a^2 + b^2]) (d - I (c + I e))) + (E^((-c + I d - I e) z) Hypergeometric2F1[(d + I (c + I e))/d, 1, (2 d + I (c + I e))/d, (b E^(I d z))/((-I) a + Sqrt[-a^2 + b^2])])/ (((-I) a + Sqrt[-a^2 + b^2]) (d + I (c + I e))) + (E^((-c + I d - I e) z) Hypergeometric2F1[(d + I (c + I e))/d, 1, (2 d + I (c + I e))/d, -((b E^(I d z))/(I a + Sqrt[-a^2 + b^2]))])/ ((I a + Sqrt[-a^2 + b^2]) (d + I (c + I e))) - (E^((c + I d - I e) z) Hypergeometric2F1[((-I) c + d - e)/d, 1, ((-I) c + 2 d - e)/d, (b E^(I d z))/((-I) a + Sqrt[-a^2 + b^2])])/ (((-I) a + Sqrt[-a^2 + b^2]) ((-I) c + d - e)) - (E^((c + I d - I e) z) Hypergeometric2F1[((-I) c + d - e)/d, 1, ((-I) c + 2 d - e)/d, -((b E^(I d z))/(I a + Sqrt[-a^2 + b^2]))])/ ((I a + Sqrt[-a^2 + b^2]) ((-I) c + d - e)))/(4 Sqrt[-a^2 + b^2]))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2002-12-18