What is the integral of x^3e^{x^4+5} ?

The integral of x^3e^{x^4+5} is 1/4 e^{x^4+5}+C

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integral of x^3e^{x^4+5}

\int x^{3} e^{x^{4} + 5} d x

\frac{1}{4} e^{x^{4} + 5} + C

Solution steps

\int x^{3} e^{x^{4} + 5} d x

Apply u-substitution

: \int \frac{e ^{u}}{4} d u

= \int \frac{e ^{u}}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{4} e^{u}

Substitute back

u = x^{4} + 5

= \frac{1}{4} e^{x^{4} + 5}

Add a constant to the solution

= \frac{1}{4} e^{x^{4} + 5} + C

y + y^{4} = (y^{6} + 3 x) y^{^{'}}

cos (x) y^{^{'}} - sin (x) y = 0

\int \frac{3 - z}{- 1 + z ^{2}} d z

cos (sin (5) x^{3})

What is the integral of x^3e^{x^4+5} ?
The integral of x^3e^{x^4+5} is 1/4 e^{x^4+5}+C