What is the integral of (e^xsin(y)+yz) ?

The integral of (e^xsin(y)+yz) is sin(y)e^x+yzx+C

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integral of (e^xsin(y)+yz)

\int (e^{x} sin (y) + yz) d x

sin (y) e^{x} + yz x + C

Solution steps

\int e^{x} sin (y) + yz d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sin (y) e^{x} d x + \int yz d x

\int sin (y) e^{x} d x = sin (y) e^{x}

\int yz d x = yz x

= sin (y) e^{x} + yz x

Add a constant to the solution

= sin (y) e^{x} + yz x + C

\int 6 cos^{3} (4 x) d x

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\int 6 (x - 1)^{2} d x

\int e^{- x - 2} d x

What is the integral of (e^xsin(y)+yz) ?
The integral of (e^xsin(y)+yz) is sin(y)e^x+yzx+C