What is the integral of (pix^3+1)^43pix^2 ?

The integral of (pix^3+1)^43pix^2 is 1/5 (pix^3+1)^5+C

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integral of (pix^3+1)^43pix^2

\int (π x^{3} + 1)^{4} 3 π x^{2} d x

\frac{1}{5} (π x^{3} + 1)^{5} + C

Solution steps

\int (π x^{3} + 1)^{4} \cdot 3 π x^{2} d x

Take the constant out:

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

= 3 π \cdot \int (π x^{3} + 1)^{4} x^{2} d x

Apply u-substitution

: \int \frac{u ^{4}}{3 π} d u

= 3 π \cdot \int \frac{u ^{4}}{3 π} d u

Take the constant out:

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

= 3 π \frac{1}{3 π} \cdot \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= 3 π \frac{1}{3 π} \cdot \frac{u ^{5}}{5}

Substitute back

u = π x^{3} + 1

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

Simplify

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

= \frac{1}{5} (π x^{3} + 1)^{5}

Add a constant to the solution

= \frac{1}{5} (π x^{3} + 1)^{5} + C

\frac{\partial}{\partial x} (10 - x^{2} - y^{2})

\frac{\partial}{\partial x} (ln (8 - x e^{- x}))

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

x \to 1 lim (\frac{x ^{3} + 1}{x - 1})

\frac{\partial}{\partial y} (\frac{y ^{2}}{x + 1})

What is the integral of (pix^3+1)^43pix^2 ?
The integral of (pix^3+1)^43pix^2 is 1/5 (pix^3+1)^5+C