What is the integral of (2+3x^2)/(sqrt(x^3+2x+10)) ?

The integral of (2+3x^2)/(sqrt(x^3+2x+10)) is 2sqrt(x^3+2x+10)+C

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integral of (2+3x^2)/(sqrt(x^3+2x+10))

\int \frac{2 + 3 x ^{2}}{x ^{3} + 2 x + 10} d x

2 x^{3} + 2 x + 10 + C

Solution steps

\int \frac{2 + 3 x ^{2}}{x ^{3} + 2 x + 10} 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^{3} + 2 x + 10

= 2 (x^{3} + 2 x + 10)^{\frac{1}{2}}

Apply radical rule:

a^{\frac{1}{n}} = n a

= 2 x^{3} + 2 x + 10

Add a constant to the solution

= 2 x^{3} + 2 x + 10 + C

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What is the integral of (2+3x^2)/(sqrt(x^3+2x+10)) ?
The integral of (2+3x^2)/(sqrt(x^3+2x+10)) is 2sqrt(x^3+2x+10)+C