What is the integral of 3/7 x^{-1/7} ?

The integral of 3/7 x^{-1/7} is 1/2 x^{6/7}+C

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integral of 3/7 x^{-1/7}

\int \frac{3}{7} x^{- \frac{1}{7}} d x

\frac{1}{2} x^{\frac{6}{7}} + C

Solution steps

\int \frac{3}{7} x^{- \frac{1}{7}} d x

Take the constant out:

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

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

Apply the Power Rule

: \frac{7}{6} x^{\frac{6}{7}}

= \frac{3}{7} \cdot \frac{7}{6} x^{\frac{6}{7}}

Simplify

\frac{3}{7} \cdot \frac{7}{6} x^{\frac{6}{7}} : \frac{1}{2} x^{\frac{6}{7}}

= \frac{1}{2} x^{\frac{6}{7}}

Add a constant to the solution

= \frac{1}{2} x^{\frac{6}{7}} + C

\frac{d}{d x} (\frac{x ^{2} - x}{1 + 3 x ^{2}})

k = 0 \sum \infty k! 2^{k} x^{k}

f (x) = - 3 cos (x), at x = \frac{3}{4} π

\int_{0}^{1} (\frac{4 t ^{3}}{1 + t ^{4}}) d t

\int \frac{( x ^{2} )}{( 3 + 4 x - 4 x ^{2} ) ^{\frac{3}{2}}} d x

What is the integral of 3/7 x^{-1/7} ?
The integral of 3/7 x^{-1/7} is 1/2 x^{6/7}+C