What is the integral of x^{-4}+2x+3 ?

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

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integral of x^{-4}+2x+3

\int x^{- 4} + 2 x + 3 d x

- \frac{1}{3 x ^{3}} + x^{2} + 3 x + C

Solution steps

\int x^{- 4} + 2 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 x^{- 4} d x + \int 2 x d x + \int 3 d x

\int x^{- 4} d x = - \frac{1}{3 x ^{3}}

\int 2 x d x = x^{2}

\int 3 d x = 3 x

= - \frac{1}{3 x ^{3}} + x^{2} + 3 x

Add a constant to the solution

= - \frac{1}{3 x ^{3}} + x^{2} + 3 x + C

x \to 0 lim (\frac{2 1 ^{x} - 1}{x})

\int \frac{1}{2 x ( 1 + x )} d x

y^{^{'}} = \frac{2}{3} x 1 - 9 y^{2}

f (x) = x^{2} + 2, at x = 3

\frac{d}{d x} (4 x arcsin (x))

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