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Evaluate the integral of (x2 + 4x - 7)(2x + 4) dx using u-substitution.

May 19, 2026Mathematics

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Answer

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

5 steps

Identify a suitable substitution.
Let $u = x^2 + 4x - 7$ .
Differentiate $u$ with respect to $x$ to find $du$ .
$\frac{du}{dx} = \frac{d}{dx}(x^2 + 4x - 7) = 2x + 4$
So, $du = (2x + 4)\,dx$ .
Substitute $u$ and $du$ into the integral.
$\int (x^2 + 4x - 7)(2x + 4)\,dx = \int u\,du$
Integrate with respect to $u$ .
$\int u\,du = \frac{u^{1+1}}{1+1} + C = \frac{u^2}{2} + C$
Substitute back $u = x^2 + 4x - 7$ into the result.
$\frac{(x^2 + 4x - 7)^2}{2} + C$

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