What is the integral of ye^{ty} ?

The integral of ye^{ty} is e^{ty} 1/t y-e^{ty} 1/(t^2)+C

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integral of ye^{ty}

\int y e^{t y}

e^{t y} \frac{1}{t} y - e^{t y} \frac{1}{t ^{2}} + C

Solution steps

\int y e^{t y} d y

Apply Integration By Parts

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

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

\int e^{t y} \frac{1}{t} d y = e^{t y} \frac{1}{t ^{2}}

= e^{t y} \frac{1}{t} y - e^{t y} \frac{1}{t ^{2}}

Add a constant to the solution

= e^{t y} \frac{1}{t} y - e^{t y} \frac{1}{t ^{2}} + C

\frac{\partial}{\partial x} (\frac{3 x}{( x + y ) ^{3}})

f (x) = - 2 sin (x), at x = \frac{3 π}{4}

\int \frac{x ^{5}}{u} d x

x \to 0 lim (sin (0))

\frac{\partial}{\partial x} (200 (y - x^{2}))

What is the integral of ye^{ty} ?
The integral of ye^{ty} is e^{ty} 1/t y-e^{ty} 1/(t^2)+C