What is the integral of 2e^x+2x-1 ?

The integral of 2e^x+2x-1 is 2e^x+x^2-x+C

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integral of 2e^x+2x-1

\int 2 e^{x} + 2 x - 1 d x

2 e^{x} + x^{2} - x + C

Solution steps

\int 2 e^{x} + 2 x - 1 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 e^{x} d x + \int 2 x d x - \int 1 d x

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

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

\int 1 d x = x

= 2 e^{x} + x^{2} - x

Add a constant to the solution

= 2 e^{x} + x^{2} - x + C

(x^{2} y^{3} - \frac{1}{1 + 9 x ^{2}}) d x + x^{3} y^{2} d y = 0

\frac{\partial}{\partial y} (ln (x^{4} + y) - z)

\frac{16}{( x ^{2} y ^{2} )}

\frac{d}{d y} (ln (x - 2 y))

\frac{d}{d r} (π r^{2})