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Worked solution

Integrate a squared linear term and cosine

Integrate [(3x−1)2+cos⁡(2x)][(3x-1)^2+\cos(2x)] with respect to xx.

CJC · Discussion · Question 18

Answer

19(3x−1)3+12sin⁡(2x)+C\dfrac19(3x-1)^3+\dfrac12\sin(2x)+C.

Integrate each term and compensate for inner derivatives

∫[(3x−1)2+cos⁡(2x)] dx=(3x−1)33(3)+sin⁡(2x)2+C=19(3x−1)3+12sin⁡(2x)+C\displaystyle\int[(3x-1)^2+\cos(2x)]\,dx=\dfrac{(3x-1)^3}{3(3)}+\dfrac{\sin(2x)}2+C=\dfrac19(3x-1)^3+\dfrac12\sin(2x)+C. Differentiating this result recovers the integrand.

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Common mistakes

Include the constant of integration and use radians for these calculus identities.

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