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Popular >

integral of ye^y-ye

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

y^{''}+4y=csc^2(2t)

y^{^{''}} + 4 y = csc^{2} (2 t)

integral of 14sin^2(x)cos^2(x)

\int 14 sin^{2} (x) cos^{2} (x) d x

limit as n approaches infinity of \sqrt[n]{cos((npi)/2)}

limit as x approaches 0 of sqrt(0)

x \to 0 lim (0)

integral of sin(x)*cos^3(x)

\int sin (x) \cdot cos^{3} (x) d x

Frequently Asked Questions (FAQ)

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