What is the integral of y^2(7-y^3)^{2/3} ?

The integral of y^2(7-y^3)^{2/3} is -1/5 (7-y^3)^{5/3}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of y^2(7-y^3)^{2/3}

\int y^{2} (7 - y^{3})^{\frac{2}{3}} d y

- \frac{1}{5} (7 - y^{3})^{\frac{5}{3}} + C

Solution steps

\int y^{2} (7 - y^{3})^{\frac{2}{3}} d y

Apply u-substitution

: \int - \frac{u ^{\frac{2}{3}}}{3} d u

= \int - \frac{u ^{\frac{2}{3}}}{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^{\frac{2}{3}} d u

Apply the Power Rule

: \frac{3}{5} u^{\frac{5}{3}}

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

Substitute back

u = 7 - y^{3}

= - \frac{1}{3} \cdot \frac{3}{5} (7 - y^{3})^{\frac{5}{3}}

Simplify

- \frac{1}{3} \cdot \frac{3}{5} (7 - y^{3})^{\frac{5}{3}} : - \frac{1}{5} (7 - y^{3})^{\frac{5}{3}}

= - \frac{1}{5} (7 - y^{3})^{\frac{5}{3}}

Add a constant to the solution

= - \frac{1}{5} (7 - y^{3})^{\frac{5}{3}} + C

9 (x^{2} + 5 x)^{2} (2 x + 5)

y = \frac{16}{x}

(7^{x})^{4}

y (θ) = e tan (θ)

\frac{d y}{d x} - 3 y = - 6

What is the integral of y^2(7-y^3)^{2/3} ?
The integral of y^2(7-y^3)^{2/3} is -1/5 (7-y^3)^{5/3}+C