What is the integral of 7/(4sqrt(x^6)) ?

The integral of 7/(4sqrt(x^6)) is -7/(8x^2)+C

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integral of 7/(4sqrt(x^6))

\int \frac{7}{4 x ^{6}} d x

- \frac{7}{8 x ^{2}} + C

Solution steps

\int \frac{7}{4 x ^{6}} d x

Take the constant out:

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

= \frac{7}{4} \cdot \int \frac{1}{x ^{6}} d x

x^{6} = x^{3},

assuming

x \geq 0

= \frac{7}{4} \cdot \int \frac{1}{x ^{3}} d x

Apply the Power Rule

: - \frac{1}{2 x ^{2}}

= \frac{7}{4} (- \frac{1}{2 x ^{2}})

Simplify

\frac{7}{4} (- \frac{1}{2 x ^{2}}) : - \frac{7}{8 x ^{2}}

= - \frac{7}{8 x ^{2}}

Add a constant to the solution

= - \frac{7}{8 x ^{2}} + C

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What is the integral of 7/(4sqrt(x^6)) ?
The integral of 7/(4sqrt(x^6)) is -7/(8x^2)+C