What is the integral of cos(x)+e^x-2x ?

The integral of cos(x)+e^x-2x is sin(x)+e^x-x^2+C

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integral of cos(x)+e^x-2x

\int cos (x) + e^{x} - 2 x d x

sin (x) + e^{x} - x^{2} + C

Solution steps

\int cos (x) + e^{x} - 2 x 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 cos (x) d x + \int e^{x} d x - \int 2 x d x

\int cos (x) d x = sin (x)

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

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

= sin (x) + e^{x} - x^{2}

Add a constant to the solution

= sin (x) + e^{x} - x^{2} + C

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

\int \frac{e ^{x}}{7 + e ^{2 x}} d x

\int sin (x + 1) d x

\int 1 - cos (θ) d θ

\int e^{x} - \frac{1}{x} d x

What is the integral of cos(x)+e^x-2x ?
The integral of cos(x)+e^x-2x is sin(x)+e^x-x^2+C