What is the integral of (27x^8-9x^2)/(e^{x^9-x^3)} ?

The integral of (27x^8-9x^2)/(e^{x^9-x^3)} is -3/(e^{x^9-x^3)}+C

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integral of (27x^8-9x^2)/(e^{x^9-x^3)}

\int \frac{27 x ^{8} - 9 x ^{2}}{e ^{x^{9} - x^{3}}} d x

- \frac{3}{e ^{x^{9} - x^{3}}} + C

Solution steps

\int \frac{27 x ^{8} - 9 x ^{2}}{e ^{x^{9} - x^{3}}} d x

Apply u-substitution

: \int \frac{3}{e ^{u}} d u

= \int \frac{3}{e ^{u}} d u

Take the constant out:

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

= 3 \cdot \int \frac{1}{e ^{u}} d u

Apply u-substitution

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

= 3 \cdot \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= 3 (- \frac{1}{v})

Substitute back

= 3 (- \frac{1}{e ^{x^{9} - x^{3}}})

Simplify

3 (- \frac{1}{e ^{x^{9} - x^{3}}}) : - \frac{3}{e ^{x^{9} - x^{3}}}

= - \frac{3}{e ^{x^{9} - x^{3}}}

Add a constant to the solution

= - \frac{3}{e ^{x^{9} - x^{3}}} + C

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What is the integral of (27x^8-9x^2)/(e^{x^9-x^3)} ?
The integral of (27x^8-9x^2)/(e^{x^9-x^3)} is -3/(e^{x^9-x^3)}+C