What is the integral of e^{-x^8}(-8x^7) ?

The integral of e^{-x^8}(-8x^7) is e^{-x^8}+C

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integral of e^{-x^8}(-8x^7)

\int e^{- x^{8}} (- 8 x^{7}) d x

e^{- x^{8}} + C

Solution steps

\int e^{- x^{8}} (- 8 x^{7}) d x

Simplify

= \int - 8 e^{- x^{8}} x^{7} d x

Take the constant out:

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

= - 8 \cdot \int e^{- x^{8}} x^{7} d x

Apply u-substitution

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

= - 8 \cdot \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

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

Use the common integral:

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

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

Substitute back

u = - x^{8}

= - 8 (- \frac{1}{8} e^{- x^{8}})

Simplify

- 8 (- \frac{1}{8} e^{- x^{8}}) : e^{- x^{8}}

= e^{- x^{8}}

Add a constant to the solution

= e^{- x^{8}} + C

\int tan^{2} (θ) cos (θ) d θ

x \to 16 lim (\frac{x ^{2}}{2} - \frac{8}{x})

\frac{d}{d x} ((3 x + 2)^{5})

f (x) = 8 π x^{2}

\frac{\partial ^{2}}{\partial y ^{2}} (\frac{x y}{x - y})

What is the integral of e^{-x^8}(-8x^7) ?
The integral of e^{-x^8}(-8x^7) is e^{-x^8}+C