What is the integral of (x^2)/((1+x^3)^{1.2)} ?

The integral of (x^2)/((1+x^3)^{1.2)} is -(1.66666…)/((1+x^3)^{0.2)}+C

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integral of (x^2)/((1+x^3)^{1.2)}

\int \frac{x ^{2}}{( 1 + x ^{3} ) ^{1.2}} d x

- \frac{1.66666 \dots}{( 1 + x ^{3} ) ^{0.2}} + C

Solution steps

\int \frac{x ^{2}}{( 1 + x ^{3} ) ^{1.2}} d x

Apply u-substitution

: \int \frac{1}{3 u ^{1.2}} d u

= \int \frac{1}{3 u ^{1.2}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int \frac{1}{u ^{1.2}} d u

Apply the Power Rule

: - \frac{5}{u ^{0.2}}

= \frac{1}{3} (- \frac{5}{u ^{0.2}})

Substitute back

u = 1 + x^{3}

= \frac{1}{3} (- \frac{5}{( 1 + x ^{3} ) ^{0.2}})

Simplify

\frac{1}{3} (- \frac{5}{( 1 + x ^{3} ) ^{0.2}}) : - \frac{1.66666 \dots}{( 1 + x ^{3} ) ^{0.2}}

= - \frac{1.66666 \dots}{( 1 + x ^{3} ) ^{0.2}}

Add a constant to the solution

= - \frac{1.66666 \dots}{( 1 + x ^{3} ) ^{0.2}} + C

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What is the integral of (x^2)/((1+x^3)^{1.2)} ?
The integral of (x^2)/((1+x^3)^{1.2)} is -(1.66666…)/((1+x^3)^{0.2)}+C