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

The integral of (7x^6+x/7) is x^7+(x^2)/(14)+C

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

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

x^{7} + \frac{x ^{2}}{14} + C

Solution steps

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

\int 7 x^{6} d x = x^{7}

\int \frac{x}{7} d x = \frac{x ^{2}}{14}

= x^{7} + \frac{x ^{2}}{14}

Add a constant to the solution

= x^{7} + \frac{x ^{2}}{14} + C

What is the integral of (7x^6+x/7) ?
The integral of (7x^6+x/7) is x^7+(x^2)/(14)+C