What is the integral of (x^5+2)^9x^4 ?

The integral of (x^5+2)^9x^4 is 1/50 (x^5+2)^{10}+C

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integral of (x^5+2)^9x^4

\int (x^{5} + 2)^{9} x^{4} d x

\frac{1}{50} (x^{5} + 2)^{10} + C

Solution steps

\int (x^{5} + 2)^{9} x^{4} d x

Apply u-substitution

: \int \frac{( u + 2 ) ^{9}}{5} d u

= \int \frac{( u + 2 ) ^{9}}{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 (u + 2)^{9} d u

Apply u-substitution

: \int v^{9} d v

= \frac{1}{5} \cdot \int v^{9} d v

Apply the Power Rule

: \frac{v ^{10}}{10}

= \frac{1}{5} \cdot \frac{v ^{10}}{10}

Substitute back

= \frac{1}{5} \cdot \frac{( x ^{5} + 2 ) ^{10}}{10}

Simplify

\frac{1}{5} \cdot \frac{( x ^{5} + 2 ) ^{10}}{10} : \frac{1}{50} (x^{5} + 2)^{10}

= \frac{1}{50} (x^{5} + 2)^{10}

Add a constant to the solution

= \frac{1}{50} (x^{5} + 2)^{10} + C

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What is the integral of (x^5+2)^9x^4 ?
The integral of (x^5+2)^9x^4 is 1/50 (x^5+2)^{10}+C