What is the integral of 3t\sqrt[3]{2t^2-11} ?

The integral of 3t\sqrt[3]{2t^2-11} is 9/16 (2t^2-11)^{4/3}+C

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integral of 3t\sqrt[3]{2t^2-11}

\frac{9}{16} (2 t^{2} - 11)^{\frac{4}{3}} + C

Solution steps

Take the constant out:

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

Apply u-substitution

Take the constant out:

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

Apply u-substitution

Take the constant out:

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

Apply the Power Rule

= 3 \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{3}{4} v^{\frac{4}{3}}

Substitute back

= 3 \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{3}{4} (2 t^{2} - 11)^{\frac{4}{3}}

Simplify

3 \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{3}{4} (2 t^{2} - 11)^{\frac{4}{3}} : \frac{9}{16} (2 t^{2} - 11)^{\frac{4}{3}}

= \frac{9}{16} (2 t^{2} - 11)^{\frac{4}{3}}

Add a constant to the solution

= \frac{9}{16} (2 t^{2} - 11)^{\frac{4}{3}} + C

What is the integral of 3t\sqrt[3]{2t^2-11} ?
The integral of 3t\sqrt[3]{2t^2-11} is 9/16 (2t^2-11)^{4/3}+C