What is the integral of (2x^7+x)/(x^4) ?

The integral of (2x^7+x)/(x^4) is (x^4)/2-1/(2x^2)+C

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integral of (2x^7+x)/(x^4)

\int \frac{2 x ^{7} + x}{x ^{4}} d x

\frac{x ^{4}}{2} - \frac{1}{2 x ^{2}} + C

Solution steps

\int \frac{2 x ^{7} + x}{x ^{4}} d x

Simplify

\frac{2 x ^{7} + x}{x ^{4}} : \frac{2 x ^{6} + 1}{x ^{3}}

= \int \frac{2 x ^{6} + 1}{x ^{3}} d x

Expand

\frac{2 x ^{6} + 1}{x ^{3}} : 2 x^{3} + \frac{1}{x ^{3}}

= \int 2 x^{3} + \frac{1}{x ^{3}} 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 2 x^{3} d x + \int \frac{1}{x ^{3}} d x

\int 2 x^{3} d x = \frac{x ^{4}}{2}

\int \frac{1}{x ^{3}} d x = - \frac{1}{2 x ^{2}}

= \frac{x ^{4}}{2} - \frac{1}{2 x ^{2}}

Add a constant to the solution

= \frac{x ^{4}}{2} - \frac{1}{2 x ^{2}} + C

\int_{0}^{3} x^{2} + 1 d x

\frac{d}{d x} (- sin (x) ln (cos (x)) + x cos (x))

y = e^{- 15 x}

\frac{d}{d x} (tan (x) sec (x))

sin (x) + \frac{8}{7} cot (x)

What is the integral of (2x^7+x)/(x^4) ?
The integral of (2x^7+x)/(x^4) is (x^4)/2-1/(2x^2)+C