What is the integral of (5x^4-2)/(sqrt(x^5-2x+11)) ?

The integral of (5x^4-2)/(sqrt(x^5-2x+11)) is 2sqrt(x^5-2x+11)+C

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integral of (5x^4-2)/(sqrt(x^5-2x+11))

\int \frac{5 x ^{4} - 2}{x ^{5} - 2 x + 11} d x

2 x^{5} - 2 x + 11 + C

Solution steps

\int \frac{5 x ^{4} - 2}{x ^{5} - 2 x + 11} d x

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 2 u^{\frac{1}{2}}

Substitute back

u = x^{5} - 2 x + 11

= 2 (x^{5} - 2 x + 11)^{\frac{1}{2}}

Apply radical rule:

= 2 x^{5} - 2 x + 11

Add a constant to the solution

= 2 x^{5} - 2 x + 11 + C

y^{^{'}} + 3 y = e^{5 t}

x \to - 2 lim (- \frac{x ^{2} - 4}{x + 2})

\int x e^{m x} d x

x \to 0 lim (\frac{e ^{5 x} - 1}{x})

\int cos (5 x) sin (x) sin (8 x) d x

What is the integral of (5x^4-2)/(sqrt(x^5-2x+11)) ?
The integral of (5x^4-2)/(sqrt(x^5-2x+11)) is 2sqrt(x^5-2x+11)+C