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

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

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

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

ln x^{7} + 6 x + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x^{7} + 6 x

= ln x^{7} + 6 x

Add a constant to the solution

= ln x^{7} + 6 x + C

\int e^{10 x} - 9 d x

n = 3 \sum \infty \frac{2}{5 ^{n}}

x \to 0 + lim (x + ∣ x ∣)

\frac{d}{d x} ((3 x^{2} + 4)^{2} (4 x^{2} - 8)^{2})

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (1) = 0, y^{^{'}} (1) = 1

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