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Popular >

integral of (-e^x+x)

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of 4sin(x/2)

\int 4 sin (\frac{x}{2}) d x

integral of (x^3-3x^2+2x)

\int (x^{3} - 3 x^{2} + 2 x) d x

integral of (x+(arccos(3x))^2)/(sqrt(1-9x^2))

\int \frac{x + ( arccos ( 3 x ) ) ^{2}}{1 - 9 x ^{2}} d x

integral of 5/(x^3+x)

\int \frac{5}{x ^{3} + x} d x

integral of 4sqrt(x)-9\sqrt[3]{x}

Frequently Asked Questions (FAQ)

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