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Popular >

integral of 4e^x-x

Solution

\int 4 e^{x} - x d x

Solution

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

Solution steps

\int 4 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 4 e^{x} d x - \int x d x

\int 4 e^{x} d x = 4 e^{x}

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

= 4 e^{x} - \frac{x ^{2}}{2}

Add a constant to the solution

= 4 e^{x} - \frac{x ^{2}}{2} + C

Graph

Popular Examples

integral of 1/(x^3+4x^2+5x)

\int \frac{1}{x ^{3} + 4 x ^{2} + 5 x} d x

integral of ((1-x)^3)/(x*\sqrt[3]{x)}

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

integral of 9/(sqrt(x+1)+\sqrt{x)}

\int \frac{9}{x + 1 + x} d x

integral of sqrt((x-7)^3)

\int (x - 7)^{3} d x

integral of (sqrt(x)+3)

\int (x + 3) d x

Frequently Asked Questions (FAQ)

What is the integral of 4e^x-x ?
The integral of 4e^x-x is 4e^x-(x^2)/2+C