What is the integral of (x^4+1)e^{x^5+5x} ?

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

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integral of (x^4+1)e^{x^5+5x}

\int (x^{4} + 1) e^{x^{5} + 5 x} d x

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

Solution steps

\int (x^{4} + 1) e^{x^{5} + 5 x} d x

Apply u-substitution

: \int \frac{e ^{u}}{5} d u

= \int \frac{e ^{u}}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{5} e^{u}

Substitute back

u = x^{5} + 5 x

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

Add a constant to the solution

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

n = 1 \sum \infty \frac{1}{( 2 n ) !}

x \to 0 lim ((1 - 6 x)^{\frac{1}{x}})

f (x) = 4 sec (x), at x = \frac{π}{3}

\int \frac{k}{x ^{3}} d x

\frac{d}{d x} (tan (3 x^{4}))

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