What is the integral of t^6e^{-t^7} ?

The integral of t^6e^{-t^7} is -1/7 e^{-t^7}+C

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integral of t^6e^{-t^7}

\int t^{6} e^{- t^{7}} d t

- \frac{1}{7} e^{- t^{7}} + C

Solution steps

\int t^{6} e^{- t^{7}} d t

Apply u-substitution

: \int - \frac{e ^{u}}{7} d u

= \int - \frac{e ^{u}}{7} d u

Take the constant out:

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

= - \frac{1}{7} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{7} e^{u}

Substitute back

u = - t^{7}

= - \frac{1}{7} e^{- t^{7}}

Add a constant to the solution

= - \frac{1}{7} e^{- t^{7}} + C

\int \frac{1}{v ^{2} - 1} d v

\frac{d}{d x} (ln (x - 1))

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

y = \frac{7}{ln ( x )}

\frac{d}{d x} (\frac{5 x}{6})

What is the integral of t^6e^{-t^7} ?
The integral of t^6e^{-t^7} is -1/7 e^{-t^7}+C