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Popular >

integral of ye^y-y

Solution

\int y e^{y} - y d y

Solution

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

Solution steps

\int y e^{y} - y d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int y e^{y} d y - \int y d y

\int y e^{y} d y = e^{y} y - e^{y}

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

= e^{y} y - e^{y} - \frac{y ^{2}}{2}

Add a constant to the solution

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

Graph

Popular Examples

integral of 5/(sqrt(x^2-x+1))

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

integral of ((sin(x))^3)/(cos(x)+2)

\int \frac{( sin ( x ) ) ^{3}}{cos ( x ) + 2} d x

integral of-6t^{1/2}+7

\int - 6 t^{\frac{1}{2}} + 7 d t

integral of (x^3+1)^43x^2

\int (x^{3} + 1)^{4} 3 x^{2} d x

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

\int \frac{3 + x}{9 - x ^{2}} d x

Frequently Asked Questions (FAQ)

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