What is the integral of x^5+1/(x^7) ?

The integral of x^5+1/(x^7) is (x^6)/6-1/(6x^6)+C

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integral of x^5+1/(x^7)

\int x^{5} + \frac{1}{x ^{7}} d x

\frac{x ^{6}}{6} - \frac{1}{6 x ^{6}} + C

Solution steps

\int x^{5} + \frac{1}{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^{5} d x + \int \frac{1}{x ^{7}} d x

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

\int \frac{1}{x ^{7}} d x = - \frac{1}{6 x ^{6}}

= \frac{x ^{6}}{6} - \frac{1}{6 x ^{6}}

Add a constant to the solution

= \frac{x ^{6}}{6} - \frac{1}{6 x ^{6}} + C

sin (100 t + 30)

\frac{d}{d x} f (x) = 2 x - 7

\frac{\partial}{\partial u} (sin (v) cos (u))

\frac{1}{s ^{4} + s ^{3}}

x \to - \infty lim (\frac{8 x ^{2} + 7 x ^{\frac{1}{3}}}{16 x ^{4} + 6})

What is the integral of x^5+1/(x^7) ?
The integral of x^5+1/(x^7) is (x^6)/6-1/(6x^6)+C