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Popular >

integral of 2x-e^x

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of x^{-7/2}

\int x^{- \frac{7}{2}} d x

integral of (t-4)/t

\int \frac{t - 4}{t} d t

integral of (e^{2x})/(36+e^{2x)}

\int \frac{e ^{2 x}}{36 + e ^{2 x}} d x

integral of sqrt(30x-9x^2-21)

\int 30 x - 9 x^{2} - 21 d x

integral of 1/(x^4+x^6)

\int \frac{1}{x ^{4} + x ^{6}} d x

Frequently Asked Questions (FAQ)

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