What is the integral of 21t^6e^{-t^7} ?

The integral of 21t^6e^{-t^7} is -3e^{-t^7}+C

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integral of 21t^6e^{-t^7}

\int 21 t^{6} e^{- t^{7}} d t

- 3 e^{- t^{7}} + C

Solution steps

\int 21 t^{6} e^{- t^{7}} d t

Take the constant out:

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

= 21 \cdot \int t^{6} e^{- t^{7}} d t

Apply u-substitution

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

= 21 \cdot \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

= 21 (- \frac{1}{7} \cdot \int e^{u} d u)

Use the common integral:

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

= 21 (- \frac{1}{7} e^{u})

Substitute back

u = - t^{7}

= 21 (- \frac{1}{7} e^{- t^{7}})

Simplify

21 (- \frac{1}{7} e^{- t^{7}}) : - 3 e^{- t^{7}}

= - 3 e^{- t^{7}}

Add a constant to the solution

= - 3 e^{- t^{7}} + C

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What is the integral of 21t^6e^{-t^7} ?
The integral of 21t^6e^{-t^7} is -3e^{-t^7}+C