What is the integral of (2x^6+1)/(2x^7+7x) ?

The integral of (2x^6+1)/(2x^7+7x) is 1/7 ln|2x^7+7x|+C

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integral of (2x^6+1)/(2x^7+7x)

\int \frac{2 x ^{6} + 1}{2 x ^{7} + 7 x} d x

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

Solution steps

\int \frac{2 x ^{6} + 1}{2 x ^{7} + 7 x} d x

Apply u-substitution

: \int \frac{1}{7 u} d u

= \int \frac{1}{7 u} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{7} ln ∣ u ∣

Substitute back

u = 2 x^{7} + 7 x

= \frac{1}{7} ln 2 x^{7} + 7 x

Add a constant to the solution

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

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What is the integral of (2x^6+1)/(2x^7+7x) ?
The integral of (2x^6+1)/(2x^7+7x) is 1/7 ln|2x^7+7x|+C