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

The integral of (2-7t)^{2/3} is -3/35 (2-7t)^{5/3}+C

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

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

- \frac{3}{35} (2 - 7 t)^{\frac{5}{3}} + C

Solution steps

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

Apply u-substitution

: \int - \frac{u ^{\frac{2}{3}}}{7} d u

= \int - \frac{u ^{\frac{2}{3}}}{7} d u

Take the constant out:

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

= - \frac{1}{7} \cdot \int u^{\frac{2}{3}} d u

Apply the Power Rule

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

= - \frac{1}{7} \cdot \frac{3}{5} u^{\frac{5}{3}}

Substitute back

u = 2 - 7 t

= - \frac{1}{7} \cdot \frac{3}{5} (2 - 7 t)^{\frac{5}{3}}

Simplify

- \frac{1}{7} \cdot \frac{3}{5} (2 - 7 t)^{\frac{5}{3}} : - \frac{3}{35} (2 - 7 t)^{\frac{5}{3}}

= - \frac{3}{35} (2 - 7 t)^{\frac{5}{3}}

Add a constant to the solution

= - \frac{3}{35} (2 - 7 t)^{\frac{5}{3}} + C

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What is the integral of (2-7t)^{2/3} ?
The integral of (2-7t)^{2/3} is -3/35 (2-7t)^{5/3}+C