Integration by Substitution

AP Calculus AB· difficulty 3/5

xex2dx=\displaystyle\int x e^{x^2}\,dx =

  • A

    ex22+C\dfrac{e^{x^2}}{2} + C

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  • B

    ex2/x+Ce^{x^2}/x + C

  • C

    ex2+Ce^{x^2} + C

  • D

    xex2+Cx e^{x^2} + C

Explanation

u=x2u = x^2, du=2xdxdu = 2x\,dx. eudu/2=eu/2\int e^u\,du/2 = e^u/2.

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