en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 6e^x-x

Solution

\int 6 e^{x} - x d x

Solution

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

Solution steps

\int 6 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 6 e^{x} d x - \int x d x

\int 6 e^{x} d x = 6 e^{x}

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

= 6 e^{x} - \frac{x ^{2}}{2}

Add a constant to the solution

= 6 e^{x} - \frac{x ^{2}}{2} + C

Graph

Popular Examples

integral of (10x)/(x^2+7x+6)

\int \frac{10 x}{x ^{2} + 7 x + 6} d x

integral of (1/(x(ln(x))^2))

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

integral of (6x^2+10x+2)/(x^3+3x^2+2x)

\int \frac{6 x ^{2} + 10 x + 2}{x ^{3} + 3 x ^{2} + 2 x} d x

integral of sin^5(8x)cos^2(8x)

\int sin^{5} (8 x) cos^{2} (8 x) d x

integral of 8/x integral

\frac{8}{x}

Frequently Asked Questions (FAQ)

What is the integral of 6e^x-x ?
The integral of 6e^x-x is 6e^x-(x^2)/2+C