What is the integral of (x^8-(2x^5)/7-sqrt(5)) ?

The integral of (x^8-(2x^5)/7-sqrt(5)) is (x^9)/9-(x^6)/(21)-sqrt(5)x+C

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integral of (x^8-(2x^5)/7-sqrt(5))

\int (x^{8} - \frac{2 x ^{5}}{7} - 5) d x

\frac{x ^{9}}{9} - \frac{x ^{6}}{21} - 5 x + C

Solution steps

\int x^{8} - \frac{2 x ^{5}}{7} - 5 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^{8} d x - \int \frac{2 x ^{5}}{7} d x - \int 5 d x

\int x^{8} d x = \frac{x ^{9}}{9}

\int \frac{2 x ^{5}}{7} d x = \frac{x ^{6}}{21}

\int 5 d x = 5 x

= \frac{x ^{9}}{9} - \frac{x ^{6}}{21} - 5 x

Add a constant to the solution

= \frac{x ^{9}}{9} - \frac{x ^{6}}{21} - 5 x + C

y^{^{'}} = \frac{x ^{2} + x y + y ^{2}}{x ^{2}}

d y = (x - 2 x y) d x

x^{2} + 4 x - 8

x \to 0 + lim (x^{5} ln (x))

x \to 1 - lim (6 x - 2)

What is the integral of (x^8-(2x^5)/7-sqrt(5)) ?
The integral of (x^8-(2x^5)/7-sqrt(5)) is (x^9)/9-(x^6)/(21)-sqrt(5)x+C