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Popular >

integral of 2+ye^y

Solution

\int 2 + y e^{y} d y

Solution

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

Solution steps

\int 2 + y 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 2 d y + \int y e^{y} d y

\int 2 d y = 2 y

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

= 2 y + e^{y} y - e^{y}

Add a constant to the solution

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

Popular Examples

limit as x approaches 0-of x/(sin(3x))

x \to 0 - lim (\frac{x}{sin ( 3 x )})

integral from-4 to 4 of xsqrt(16-x^2)

\int_{- 4}^{4} x 16 - x^{2} d x

tangent of g(x)= 1/(2sqrt(x)),\at x=9 tangent of

g (x) = \frac{1}{2 x}, at x = 9

area x^{1/2},x-2,[0,4]area

x^{\frac{1}{2}}, x - 2, [0, 4]

7x-4ysqrt(x^2+1)(dy)/(dx)=0,y(0)=6

7 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0, y (0) = 6

Frequently Asked Questions (FAQ)

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