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

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

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

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

ln x^{7} + 2 x + C

Solution steps

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

= ln x^{7} + 2 x

Add a constant to the solution

= ln x^{7} + 2 x + C

2 x^{2}

\int_{- 2}^{- 1} (u - \frac{1}{u ^{2}}) d u

1 + x^{2}

\frac{d y}{d x} = e^{2 x} (1 + y^{2})

y = 3 x^{2} + 5

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