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Integration by Substitution

AP Calculus AB· difficulty 2/5

∫2x(x2+1)3 dx=\displaystyle\int 2x(x^2 + 1)^3\,dx =

  • A

    (x2+1)4+C(x^2+1)^4 + C

  • B

    x44+C\dfrac{x^4}{4} + C

  • C

    (x2+1)33+C\dfrac{(x^2+1)^3}{3} + C

  • D

    (x2+1)44+C\dfrac{(x^2+1)^4}{4} + C

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Explanation

u=x2+1u = x^2 + 1, du=2x dxdu = 2x\,dx. ∫u3 du=u4/4\int u^3\,du = u^4/4.

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