What is the integral of x^2(x^3+5)^9 ?

The integral of x^2(x^3+5)^9 is 1/30 (x^3+5)^{10}+C

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integral of x^2(x^3+5)^9

\int x^{2} (x^{3} + 5)^{9} d x

\frac{1}{30} (x^{3} + 5)^{10} + C

Solution steps

\int x^{2} (x^{3} + 5)^{9} d x

Apply u-substitution

: \int \frac{u ^{9}}{3} d u

= \int \frac{u ^{9}}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int u^{9} d u

Apply the Power Rule

: \frac{u ^{10}}{10}

= \frac{1}{3} \cdot \frac{u ^{10}}{10}

Substitute back

u = x^{3} + 5

= \frac{1}{3} \cdot \frac{( x ^{3} + 5 ) ^{10}}{10}

Simplify

\frac{1}{3} \cdot \frac{( x ^{3} + 5 ) ^{10}}{10} : \frac{1}{30} (x^{3} + 5)^{10}

= \frac{1}{30} (x^{3} + 5)^{10}

Add a constant to the solution

= \frac{1}{30} (x^{3} + 5)^{10} + C

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{3} - x})

\int \frac{3 - 6 x}{25 - 9 x ^{2}} d x

\frac{\partial}{\partial x} ((x + y) e^{3 x - 4 y})

\frac{d ^{2}}{d x ^{2}} (\frac{e ^{x}}{8 x + 1})

ln (ln (x^{2}))

What is the integral of x^2(x^3+5)^9 ?
The integral of x^2(x^3+5)^9 is 1/30 (x^3+5)^{10}+C