What is the integral of x^7-4x^{-3}+1 ?

The integral of x^7-4x^{-3}+1 is (x^8)/8+2/(x^2)+x+C

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integral of x^7-4x^{-3}+1

\int x^{7} - 4 x^{- 3} + 1 d x

\frac{x ^{8}}{8} + \frac{2}{x ^{2}} + x + C

Solution steps

\int x^{7} - 4 x^{- 3} + 1 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^{7} d x - \int 4 x^{- 3} d x + \int 1 d x

\int x^{7} d x = \frac{x ^{8}}{8}

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

\int 1 d x = x

= \frac{x ^{8}}{8} - (- \frac{2}{x ^{2}}) + x

Simplify

= \frac{x ^{8}}{8} + \frac{2}{x ^{2}} + x

Add a constant to the solution

= \frac{x ^{8}}{8} + \frac{2}{x ^{2}} + x + C

\int 4 x e^{- x^{2}} d x

y^{^{'}} + y = - 1

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

\int_{0}^{1} (x + 1)^{3} d x

x \to - 1 lim (2 - 3 x)

What is the integral of x^7-4x^{-3}+1 ?
The integral of x^7-4x^{-3}+1 is (x^8)/8+2/(x^2)+x+C