16. e* (sinx + cosx)

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Solution

The given function is e x ( sinx+cosx ).

The given function is in the form of,

∫ e x ( f( x )+ f ′ ( x ) )dx= e x f( x )+C

Substitute the value of f( x ) is sinx and the value of f ′ ( x ) is cosx in the above formula.

Thus, the integral of the given function is ∫ e x ( sinx+cos )dx= e x sinx+C.

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