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u-Substitution (Calculus II)

Free printable university Calculus II worksheet: evaluating indefinite integrals by u-substitution, from (ax+b)^n to exponential, trig and square-root composites. Every answer key is computed and verified by differentiation.

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Calculus II · Math worksheet
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Integration Techniques: u-Substitution

Evaluate each indefinite integral by substitution: choose u so that du (up to a constant factor) appears in the integrand, rewrite the integral in u, integrate, then back-substitute. Include + C.

  1. 1.
    Evaluate the integral of (3x−4)2(3x - 4)^{2} dx using the substitution u = 3x - 4.
  2. 2.
    Evaluate the integral of 2x(x2+2)4(x^{2} + 2)^{4} dx.
  3. 3.
    Evaluate the integral of x e3x2e^{3x^{2}} dx.
  4. 4.
    Evaluate the integral of sin2(x) cos(x) dx.
  5. 5.
    Evaluate the integral of cos3(x) sin(x) dx.
  6. 6.
    Evaluate the integral of x/(x2x^{2} + 2) dx.
  7. 7.
    Evaluate the integral of x x2+2\sqrt{x^{2} + 2} dx.
  8. 8.
    Evaluate the integral of (3x+4)3(3x + 4)^{3} dx using the substitution u = 3x + 4.
  9. 9.
    Evaluate the integral of 4x(x2+3)3(x^{2} + 3)^{3} dx.
  10. 10.
    Evaluate the integral of x e2x2e^{2x^{2}} dx.
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