What is the integral of (4e^{2x}cos(yz)+3y^2) ?

The integral of (4e^{2x}cos(yz)+3y^2) is 3y^2x+2e^{2x}cos(yz)+C

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integral of (4e^{2x}cos(yz)+3y^2)

\int (4 e^{2 x} cos (yz) + 3 y^{2}) d x

3 y^{2} x + 2 e^{2 x} cos (yz) + C

Solution steps

\int 4 e^{2 x} cos (yz) + 3 y^{2} 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 3 y^{2} d x + \int 4 cos (yz) e^{2 x} d x

\int 3 y^{2} d x = 3 y^{2} x

\int 4 cos (yz) e^{2 x} d x = 2 e^{2 x} cos (yz)

= 3 y^{2} x + 2 e^{2 x} cos (yz)

Add a constant to the solution

= 3 y^{2} x + 2 e^{2 x} cos (yz) + C

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What is the integral of (4e^{2x}cos(yz)+3y^2) ?
The integral of (4e^{2x}cos(yz)+3y^2) is 3y^2x+2e^{2x}cos(yz)+C