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

The integral of (x^3-5x)^5(3x^2-5) is ((x^3-5x)^6)/6+C

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

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

\frac{( x ^{3} - 5 x ) ^{6}}{6} + C

Solution steps

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

Apply u-substitution

= \int u^{5} d u

Apply the Power Rule

= \frac{u ^{6}}{6}

Substitute back

u = x^{3} - 5 x

= \frac{( x ^{3} - 5 x ) ^{6}}{6}

Add a constant to the solution

= \frac{( x ^{3} - 5 x ) ^{6}}{6} + C

What is the integral of (x^3-5x)^5(3x^2-5) ?
The integral of (x^3-5x)^5(3x^2-5) is ((x^3-5x)^6)/6+C