Integration by Parts (LIATE) (Calculus II)
Free printable university Calculus II worksheet: integration by parts with the LIATE rule for choosing u and dv, covering x e^(ax), x sin(ax), x cos(ax), x^n ln(x) and ln(x). Every answer key is computed and verified by differentiation.
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Calculus II · Math worksheet
Name
Date
Math
Integration Techniques: Integration by Parts (LIATE)
Evaluate each integral with integration by parts: integral of u dv = uv - integral of v du. Choose u by LIATE (Logarithmic, Inverse trig, Algebraic, Trig, Exponential): u is the type that appears FIRST in the list, dv is the rest. Include + C.
- 1.Evaluate the integral of 3x dx using integration by parts.
- 2.Evaluate the integral of 3x cos(x) dx using integration by parts.
- 3.Evaluate the integral of x sin(x) dx using integration by parts.
- 4.Evaluate the integral of ln(x) dx using integration by parts (x > 0).
- 5.Evaluate the integral of ln(x) dx using integration by parts (x > 0). Hint: write the integrand as 1 . ln(x).
- 6.Evaluate the integral of 3x dx using integration by parts.
- 7.Evaluate the integral of 2x cos(3x) dx using integration by parts.
- 8.Evaluate the integral of 2x sin(3x) dx using integration by parts.
- 9.Evaluate the integral of ln(x) dx using integration by parts (x > 0).
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