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

The integral of 7x^6-6/(x^6) is x^7+6/(5x^5)+C

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

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

x^{7} + \frac{6}{5 x ^{5}} + C

Solution steps

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

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

\int \frac{6}{x ^{6}} d x = - \frac{6}{5 x ^{5}}

= x^{7} - (- \frac{6}{5 x ^{5}})

Simplify

= x^{7} + \frac{6}{5 x ^{5}}

Add a constant to the solution

= x^{7} + \frac{6}{5 x ^{5}} + C

\int 5 + 2 x d x

h \to 0 lim (\frac{( a + h ) - ( a )}{h})

n = 1 \sum \infty (5)^{- n}

\int_{- 3}^{3} sin (x) x d x

\frac{d}{d x} (x^{\frac{9}{2}})

What is the integral of 7x^6-6/(x^6) ?
The integral of 7x^6-6/(x^6) is x^7+6/(5x^5)+C