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(sin x+sinh x)dx

(sin⁡x+sinh⁡x)dx (\sin x+\sinh x) d x =

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Csc, sec, and cot of special anglesright chevron icon

Full solution

Q. (sin⁡x+sinh⁡x)dx (\sin x+\sinh x) d x =
  1. Separate Integration: To solve the integral of sin⁡x+sinh⁡x\sin x + \sinh x dx, we need to integrate each term separately.\newline\int(\sin x + \sinh x) \, dx = \int\sin x \, dx + \int\sinh x \, dx
  2. Integrate \(\sin x: Integrate sin⁡x\sin x. The integral of sin⁡x\sin x with respect to xx is −cos⁡x+C-\cos x + C, where CC is the constant of integration.\newline∫sin⁡x dx=−cos⁡x+C\int \sin x \, dx = -\cos x + C
  3. Integrate sinh⁡x\sinh x: Integrate sinh⁡x\sinh x. The integral of sinh⁡x\sinh x with respect to xx is cosh⁡x+C\cosh x + C.\newline∫sinh⁡x dx=cosh⁡x+C\int \sinh x \, dx = \cosh x + C
  4. Combine Results: Combine the results from the previous steps to get the final answer.\newline∫(sin⁡x+sinh⁡x)dx=(−cos⁡x+C)+(cosh⁡x+C)\int(\sin x + \sinh x) dx = (-\cos x + C) + (\cosh x + C)

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