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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

Graph

Popular Examples

integral of x^3(a^2-x^2)^{1/2}

\int x^{3} (a^{2} - x^{2})^{\frac{1}{2}} d x

integral of (sin(sqrt(3x)))/(sqrt(3x))

\int \frac{sin ( 3 x )}{3 x} d x

integral of x^3sqrt(x^2+39)

\int x^{3} x^{2} + 39 d x

integral of ((2x+6))/(x^2+4x+8)

\int \frac{( 2 x + 6 )}{x ^{2} + 4 x + 8} d x

integral of (x^2+6x)^{24}(x+3)

\int (x^{2} + 6 x)^{24} (x + 3) d 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