What is the integral of (x^2-3x+1)^{10}(2x-3) ?

The integral of (x^2-3x+1)^{10}(2x-3) is ((x^2-3x+1)^{11})/(11)+C

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integral of (x^2-3x+1)^{10}(2x-3)

\int (x^{2} - 3 x + 1)^{10} (2 x - 3) d x

\frac{( x ^{2} - 3 x + 1 ) ^{11}}{11} + C

Solution steps

\int (x^{2} - 3 x + 1)^{10} (2 x - 3) d x

Apply u-substitution

: \int u^{10} d u

= \int u^{10} d u

Apply the Power Rule

: \frac{u ^{11}}{11}

= \frac{u ^{11}}{11}

Substitute back

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

= \frac{( x ^{2} - 3 x + 1 ) ^{11}}{11}

Add a constant to the solution

= \frac{( x ^{2} - 3 x + 1 ) ^{11}}{11} + C

\int (x - \frac{1}{x ^{2}}) (x^{2} + \frac{2}{x})^{9} d x

\int \frac{1}{x ^{2} - 3 x - 18} d x

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

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

What is the integral of (x^2-3x+1)^{10}(2x-3) ?
The integral of (x^2-3x+1)^{10}(2x-3) is ((x^2-3x+1)^{11})/(11)+C