What is the integral of (2x-5)(x^2-5x+7)^3 ?

The integral of (2x-5)(x^2-5x+7)^3 is ((x^2-5x+7)^4)/4+C

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integral of (2x-5)(x^2-5x+7)^3

\int (2 x - 5) (x^{2} - 5 x + 7)^{3} d x

\frac{( x ^{2} - 5 x + 7 ) ^{4}}{4} + C

Solution steps

\int (2 x - 5) (x^{2} - 5 x + 7)^{3} d x

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

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

Substitute back

u = x^{2} - 5 x + 7

= \frac{( x ^{2} - 5 x + 7 ) ^{4}}{4}

Add a constant to the solution

= \frac{( x ^{2} - 5 x + 7 ) ^{4}}{4} + C

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

\int \frac{1}{t ( 1 - t )} d t

\int 26 d x

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

\int (e^{- 4 x} + 7^{x}) d x

What is the integral of (2x-5)(x^2-5x+7)^3 ?
The integral of (2x-5)(x^2-5x+7)^3 is ((x^2-5x+7)^4)/4+C