Funciones hiperbólicas sinh x = ex −e−x 2 cosh x = ex +e−x 2 tanh x = sinh x cosh x y además cosech x = 1 sinh x , sech x = 1 cosh x y cotanh x = 1 tanh x . Se tienen las siguientes igualdades: cosh2 x − sinh2 x = 1, sech2 x + tanh2 x = 1 y cotanh2 x − cosech2 x = 1. Primitivas R 1. dx = x + C R n+1 2. xn dx = xn+1 + C si n ∈ R \ {−1}. R 3. x1 dx = ln|x| + C. R n+1 4. tn dt = tn+1 + C si n ∈ R \ {−1}. R 5. 1t dt = ln|t| + C. R 6. et dt = et + C. R at + C. 7. at dt = lna R 8. cost dt = sint + C. R 9. sint dt = −costdt. R R R 10. cos12 t dt = sec2 t dt = (1 + tan2 t) dt = tant + C. R R 11. sin12 t dt = cosec2 t dt = −cott + C. R 1 12. √1−t 2 dt = arcsint + C. R 1 13. 1+t2 dt = arctant + C. R 14. cosht dt = sinht + C. R 15. sinht dt = coshtdt. R 1 16. cosh 2 t dt = tanht + C. R 1 17. sinh2 t dt = cotht + C. R 1 18. √1+t dt = arcsinht + C. 2 R 1 19. √t2 −1 dt = arccosht + C.