What is the integral of t^2e^{t/3} ?

The integral of t^2e^{t/3} is 3e^{t/3}t^2-6(3e^{t/3}t-9e^{t/3})+C

integral of t^2e^{t/3}

\int t^{2} e^{\frac{t}{3}} d t

3 e^{\frac{t}{3}} t^{2} - 6 (3 e^{\frac{t}{3}} t - 9 e^{\frac{t}{3}}) + C

Solution steps

\int t^{2} e^{\frac{t}{3}} d t

Apply Integration By Parts

= 3 e^{\frac{t}{3}} t^{2} - \int 6 e^{\frac{t}{3}} t d t

\int 6 e^{\frac{t}{3}} t d t = 6 (3 e^{\frac{t}{3}} t - 9 e^{\frac{t}{3}})

= 3 e^{\frac{t}{3}} t^{2} - 6 (3 e^{\frac{t}{3}} t - 9 e^{\frac{t}{3}})

Add a constant to the solution

= 3 e^{\frac{t}{3}} t^{2} - 6 (3 e^{\frac{t}{3}} t - 9 e^{\frac{t}{3}}) + C

x \to \infty lim (\frac{( e ^{- x y - x + y} )}{x ^{2} y ^{2} + x y})

y^{^{''}} - 2 y^{^{'}} + 8 y = 320 t^{2}

d er i v a t i v e \frac{1}{3 x}

x \to 4 lim (\frac{x + 4}{x - 4})

\int \frac{t}{e ^{3 t}} d t

What is the integral of t^2e^{t/3} ?
The integral of t^2e^{t/3} is 3e^{t/3}t^2-6(3e^{t/3}t-9e^{t/3})+C