What is the integral of t^5e^{-t^6} ?

The integral of t^5e^{-t^6} is -1/6 e^{-t^6}+C

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integral of t^5e^{-t^6}

\int t^{5} e^{- t^{6}} d t

- \frac{1}{6} e^{- t^{6}} + C

Solution steps

\int t^{5} e^{- t^{6}} d t

Apply u-substitution

: \int - \frac{e ^{u}}{6} d u

= \int - \frac{e ^{u}}{6} d u

Take the constant out:

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

= - \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{6} e^{u}

Substitute back

u = - t^{6}

= - \frac{1}{6} e^{- t^{6}}

Add a constant to the solution

= - \frac{1}{6} e^{- t^{6}} + C

\frac{d}{d x} (- 5 x + 10 x^{2})

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

x \to 1 + lim (\frac{8}{1 - x})

\frac{d}{d x} (\frac{6 x ^{2} + 6 x + 4}{x})

\int \frac{4}{x - 1} d x

What is the integral of t^5e^{-t^6} ?
The integral of t^5e^{-t^6} is -1/6 e^{-t^6}+C