What is the integral of 3x^{1/5} ?

The integral of 3x^{1/5} is 5/2 x^{6/5}+C

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integral of 3x^{1/5}

\int 3 x^{\frac{1}{5}} d x

\frac{5}{2} x^{\frac{6}{5}} + C

Solution steps

\int 3 x^{\frac{1}{5}} d x

Take the constant out:

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

= 3 \cdot \int x^{\frac{1}{5}} d x

Apply the Power Rule

: \frac{5}{6} x^{\frac{6}{5}}

= 3 \cdot \frac{5}{6} x^{\frac{6}{5}}

Simplify

3 \cdot \frac{5}{6} x^{\frac{6}{5}} : \frac{5}{2} x^{\frac{6}{5}}

= \frac{5}{2} x^{\frac{6}{5}}

Add a constant to the solution

= \frac{5}{2} x^{\frac{6}{5}} + C

y^{^{''}} + 100 y = 0

\int_{1}^{2} \frac{3}{t} d t

y = x^{2} - 3 x, (1, - 2)

y^{^{''}} + 2 y^{^{'}} + 5 y = 3 cos (x)

t y^{^{'}} + (t + 1) y = t, y (ln (2)) = 1