What is the integral of-3^4sqrt(x) ?

The integral of-3^4sqrt(x) is -54x^{3/2}+C

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integral of-3^4sqrt(x)

\int - 3^{4} x d x

- 54 x^{\frac{3}{2}} + C

Solution steps

\int - 3^{4} x d x

Take the constant out:

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

= - 3^{4} \cdot \int x d x

Simplify

= - 81 \cdot \int x d x

Apply the Power Rule

= - 81 \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

- 81 \cdot \frac{2}{3} x^{\frac{3}{2}} : - 54 x^{\frac{3}{2}}

= - 54 x^{\frac{3}{2}}

Add a constant to the solution

= - 54 x^{\frac{3}{2}} + C