What is the integral of ((1+xy)e^{xy}) ?

The integral of ((1+xy)e^{xy}) is e^{yx}x+C

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integral of ((1+xy)e^{xy})

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

e^{y x} x + C

Solution steps

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

Apply Integration By Parts

: e^{y x} \frac{1}{y} + e^{y x} x - \int e^{y x} d x

= e^{y x} \frac{1}{y} + e^{y x} x - \int e^{y x} d x

\int e^{y x} d x = \frac{1}{y} e^{y x}

= e^{y x} \frac{1}{y} + e^{y x} x - \frac{1}{y} e^{y x}

Simplify

= e^{y x} x

Add a constant to the solution

= e^{y x} x + C

y - x^{2} y = 2 - 2 x^{3}

\int \frac{7}{x ^{2} x ^{2} + 25} d x

\frac{d y}{d x} = (y - 1)^{2}

\frac{d y}{d t} = 6 y^{2}

f (x) = ln (x)

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