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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

= 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

= 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

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