What is the integral of (4x^3-2x)(x^4-x^2-5)^3 ?

The integral of (4x^3-2x)(x^4-x^2-5)^3 is ((x^4-x^2-5)^4)/4+C

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integral of (4x^3-2x)(x^4-x^2-5)^3

\int (4 x^{3} - 2 x) (x^{4} - x^{2} - 5)^{3} d x

\frac{( x ^{4} - x ^{2} - 5 ) ^{4}}{4} + C

Solution steps

\int (4 x^{3} - 2 x) (x^{4} - x^{2} - 5)^{3} d x

Apply u-substitution

= \int u^{3} d u

Apply the Power Rule

= \frac{u ^{4}}{4}

Substitute back

u = x^{4} - x^{2} - 5

= \frac{( x ^{4} - x ^{2} - 5 ) ^{4}}{4}

Add a constant to the solution

= \frac{( x ^{4} - x ^{2} - 5 ) ^{4}}{4} + C

What is the integral of (4x^3-2x)(x^4-x^2-5)^3 ?
The integral of (4x^3-2x)(x^4-x^2-5)^3 is ((x^4-x^2-5)^4)/4+C