What is the integral of t^7e^{-t^8} ?

The integral of t^7e^{-t^8} is -1/8 e^{-t^8}+C

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integral of t^7e^{-t^8}

\int t^{7} e^{- t^{8}} d t

- \frac{1}{8} e^{- t^{8}} + C

Solution steps

\int t^{7} e^{- t^{8}} d t

Apply u-substitution

: \int - \frac{e ^{u}}{8} d u

= \int - \frac{e ^{u}}{8} d u

Take the constant out:

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

= - \frac{1}{8} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{8} e^{u}

Substitute back

u = - t^{8}

= - \frac{1}{8} e^{- t^{8}}

Add a constant to the solution

= - \frac{1}{8} e^{- t^{8}} + C

x \to 2 lim (\frac{x}{2 - x})

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

\frac{d y}{d t} + e^{t} y = - 5 e^{t}

\int x^{2} y cos (x) + 2 x y sin (x) - y^{2} e^{x} d x

What is the integral of t^7e^{-t^8} ?
The integral of t^7e^{-t^8} is -1/8 e^{-t^8}+C