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

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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

= 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 4 lim (\frac{5}{x - 4})

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

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

\int \frac{4 x - 11}{x ^{3} - 9 x ^{2}} d x

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

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