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

The integral of (x^7+7x+7/x+7) is (x^8)/8+(7x^2)/2+7ln|x|+7x+C

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

\int (x^{7} + 7 x + \frac{7}{x} + 7) d x

\frac{x ^{8}}{8} + \frac{7 x ^{2}}{2} + 7 ln ∣ x ∣ + 7 x + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int x^{7} d x = \frac{x ^{8}}{8}

\int 7 x d x = \frac{7 x ^{2}}{2}

\int \frac{7}{x} d x = 7 ln ∣ x ∣

\int 7 d x = 7 x

= \frac{x ^{8}}{8} + \frac{7 x ^{2}}{2} + 7 ln ∣ x ∣ + 7 x

Add a constant to the solution

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

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What is the integral of (x^7+7x+7/x+7) ?
The integral of (x^7+7x+7/x+7) is (x^8)/8+(7x^2)/2+7ln|x|+7x+C