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Popular >

integral of 1+ye^{xy}

Solution

\int 1 + y e^{x y} d x

Solution

x + e^{y x} + C

Solution steps

\int 1 + y e^{x y} 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 1 d x + \int y e^{y x} d x

\int 1 d x = x

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

= x + e^{y x}

Add a constant to the solution

= x + e^{y x} + C

Graph

Popular Examples

integral of-8(x-1)*(1-x)

\int - 8 (x - 1) \cdot (1 - x) d x

t^2y^{''}+ty^'+9y=0

t^{2} y^{^{''}} + t y^{^{'}} + 9 y = 0

limit as h approaches-3 of (h^3+8)/(h+2)

h \to - 3 lim (\frac{h ^{3} + 8}{h + 2})

(\partial)/(\partial x)(csc(x))

\frac{\partial}{\partial x} (csc (x))

derivative of y=-3/(4x^4)+(24)/(5x^5)derivative of

y = - \frac{3}{4 x ^{4}} + \frac{24}{5 x ^{5}}

Frequently Asked Questions (FAQ)

What is the integral of 1+ye^{xy} ?
The integral of 1+ye^{xy} is x+e^{yx}+C