What is the integral of x^7e^{3x^4} ?

The integral of x^7e^{3x^4} is 1/36 (e^{3x^4}*3x^4-e^{3x^4})+C

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integral of x^7e^{3x^4}

\int x^{7} e^{3 x^{4}} d x

\frac{1}{36} (e^{3 x^{4}} \cdot 3 x^{4} - e^{3 x^{4}}) + C

Solution steps

\int x^{7} e^{3 x^{4}} d x

Apply u-substitution

: \int \frac{e ^{u} u}{36} d u

= \int \frac{e ^{u} u}{36} d u

Take the constant out:

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

= \frac{1}{36} \cdot \int e^{u} u d u

Apply Integration By Parts

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

= \frac{1}{36} (e^{u} u - \int e^{u} d u)

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

= \frac{1}{36} (e^{u} u - e^{u})

Substitute back

u = 3 x^{4}

= \frac{1}{36} (e^{3 x^{4}} \cdot 3 x^{4} - e^{3 x^{4}})

Add a constant to the solution

= \frac{1}{36} (e^{3 x^{4}} \cdot 3 x^{4} - e^{3 x^{4}}) + C

\frac{t - t}{t ^{\frac{1}{9}}}

\frac{d}{d x} (2 x^{4} - 6 x^{3} - 12 x - 8)

n = 5 \sum \infty \frac{1}{n ( n - 1 )}

\int_{2}^{4} (x^{4} - 1) d x

x \to 0 lim (\frac{1 - e ^{x}}{e ^{x}})

What is the integral of x^7e^{3x^4} ?
The integral of x^7e^{3x^4} is 1/36 (e^{3x^4}*3x^4-e^{3x^4})+C