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

The integral of 7-1/(7x^2) is 7x+1/(7x)+C

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integral of 7-1/(7x^2)

\int 7 - \frac{1}{7 x ^{2}} d x

7 x + \frac{1}{7 x} + C

Solution steps

\int 7 - \frac{1}{7 x ^{2}} 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 d x - \int \frac{1}{7 x ^{2}} d x

\int 7 d x = 7 x

\int \frac{1}{7 x ^{2}} d x = - \frac{1}{7 x}

= 7 x - (- \frac{1}{7 x})

Simplify

= 7 x + \frac{1}{7 x}

Add a constant to the solution

= 7 x + \frac{1}{7 x} + C

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