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Popular >

integral of y+xe^y

Solution

\int y + x e^{y} d y

Solution

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

Solution steps

\int y + x e^{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 d y + \int x e^{y} d y

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

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

= \frac{y ^{2}}{2} + x e^{y}

Add a constant to the solution

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

Popular Examples

limit as x approaches infinity of 1*x

x \to \infty lim (1 \cdot x)

derivative of (x^3-8/(x^3+8))

\frac{d}{d x} (\frac{x ^{3} - 8}{x ^{3} + 8})

(\partial)/(\partial x)(x^2y-y^2-7)

\frac{\partial}{\partial x} (x^{2} y - y^{2} - 7)

integral of sec^5(4x)tan(4x)

\int sec^{5} (4 x) tan (4 x) d x

limit as x approaches-1 of 10x

x \to - 1 lim (10 x)

Frequently Asked Questions (FAQ)

What is the integral of y+xe^y ?
The integral of y+xe^y is (y^2)/2+xe^y+C