What is the integral of 1/((4x)^7) ?

The integral of 1/((4x)^7) is -1/(98304x^6)+C

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integral of 1/((4x)^7)

\int \frac{1}{( 4 x ) ^{7}} d x

- \frac{1}{98304 x ^{6}} + C

Solution steps

\int \frac{1}{( 4 x ) ^{7}} d x

Simplify

\frac{1}{( 4 x ) ^{7}} : \frac{1}{16384 x ^{7}}

= \int \frac{1}{16384 x ^{7}} d x

Take the constant out:

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

= \frac{1}{16384} \cdot \int \frac{1}{x ^{7}} d x

Apply the Power Rule

: - \frac{1}{6 x ^{6}}

= \frac{1}{16384} (- \frac{1}{6 x ^{6}})

Simplify

\frac{1}{16384} (- \frac{1}{6 x ^{6}}) : - \frac{1}{98304 x ^{6}}

= - \frac{1}{98304 x ^{6}}

Add a constant to the solution

= - \frac{1}{98304 x ^{6}} + C

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What is the integral of 1/((4x)^7) ?
The integral of 1/((4x)^7) is -1/(98304x^6)+C