What is the integral of (-6x+1)(-3x^2+x-1)^{5/3} ?

The integral of (-6x+1)(-3x^2+x-1)^{5/3} is 3/8 (-3x^2+x-1)^{8/3}+C

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integral of (-6x+1)(-3x^2+x-1)^{5/3}

\int (- 6 x + 1) (- 3 x^{2} + x - 1)^{\frac{5}{3}} d x

\frac{3}{8} (- 3 x^{2} + x - 1)^{\frac{8}{3}} + C

Solution steps

\int (- 6 x + 1) (- 3 x^{2} + x - 1)^{\frac{5}{3}} d x

Apply u-substitution

: \int u^{\frac{5}{3}} d u

= \int u^{\frac{5}{3}} d u

Apply the Power Rule

: \frac{3}{8} u^{\frac{8}{3}}

= \frac{3}{8} u^{\frac{8}{3}}

Substitute back

u = - 3 x^{2} + x - 1

= \frac{3}{8} (- 3 x^{2} + x - 1)^{\frac{8}{3}}

Add a constant to the solution

= \frac{3}{8} (- 3 x^{2} + x - 1)^{\frac{8}{3}} + C

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What is the integral of (-6x+1)(-3x^2+x-1)^{5/3} ?
The integral of (-6x+1)(-3x^2+x-1)^{5/3} is 3/8 (-3x^2+x-1)^{8/3}+C