What is the integral of (2(z+1)e^{2x-2}+2y) ?

The integral of (2(z+1)e^{2x-2}+2y) is 2yx+e^{-2+2x}(1+z)+C

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integral of (2(z+1)e^{2x-2}+2y)

\int (2 (z + 1) e^{2 x - 2} + 2 y) d x

2 y x + e^{- 2 + 2 x} (1 + z) + C

Solution steps

\int 2 (z + 1) e^{2 x - 2} + 2 y 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 2 y d x + \int (1 + z) \cdot 2 e^{- 2 + 2 x} d x

\int 2 y d x = 2 y x

\int (1 + z) \cdot 2 e^{- 2 + 2 x} d x = e^{- 2 + 2 x} (1 + z)

= 2 y x + e^{- 2 + 2 x} (1 + z)

Add a constant to the solution

= 2 y x + e^{- 2 + 2 x} (1 + z) + C

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What is the integral of (2(z+1)e^{2x-2}+2y) ?
The integral of (2(z+1)e^{2x-2}+2y) is 2yx+e^{-2+2x}(1+z)+C