What is the integral of t^{24}e^{-t^{25}} ?

The integral of t^{24}e^{-t^{25}} is -1/25 e^{-t^{25}}+C

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integral of t^{24}e^{-t^{25}}

\int t^{24} e^{- t^{25}} d t

- \frac{1}{25} e^{- t^{25}} + C

Solution steps

\int t^{24} e^{- t^{25}} d t

Apply u-substitution

: \int - \frac{e ^{u}}{25} d u

= \int - \frac{e ^{u}}{25} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{25} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= - \frac{1}{25} e^{u}

Substitute back

u = - t^{25}

= - \frac{1}{25} e^{- t^{25}}

Add a constant to the solution

= - \frac{1}{25} e^{- t^{25}} + C

x \to 0 lim ((x)^{3 x})

\int \frac{x ^{3} + x + 1}{x ( x ^{2} + 1 )} d x

y = 9 x, y = x^{2} - 10

x^{4}, at x = - \frac{1}{3}

\int_{0}^{1} 3 e^{- 3 t} d t

What is the integral of t^{24}e^{-t^{25}} ?
The integral of t^{24}e^{-t^{25}} is -1/25 e^{-t^{25}}+C