What is the integral of t^{19}e^{-t^{20}} ?

The integral of t^{19}e^{-t^{20}} is -1/20 e^{-t^{20}}+C

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integral of t^{19}e^{-t^{20}}

\int t^{19} e^{- t^{20}} d t

- \frac{1}{20} e^{- t^{20}} + C

Solution steps

\int t^{19} e^{- t^{20}} d t

Apply u-substitution

: \int - \frac{e ^{u}}{20} d u

= \int - \frac{e ^{u}}{20} d u

Take the constant out:

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

= - \frac{1}{20} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{20} e^{u}

Substitute back

u = - t^{20}

= - \frac{1}{20} e^{- t^{20}}

Add a constant to the solution

= - \frac{1}{20} e^{- t^{20}} + C

\frac{5}{s ^{3} - 2 s ^{2} - 3 s}

(2005, 56), (2010, 59)

\int_{0}^{1} \frac{3}{x ^{2} - x - 2} d x

\frac{3}{x ^{2}}

n = 1 \sum \infty (- 1)^{n} e^{- n}

What is the integral of t^{19}e^{-t^{20}} ?
The integral of t^{19}e^{-t^{20}} is -1/20 e^{-t^{20}}+C