Tim Gan Math
Sign up free

u-Substitution Method (Cancelling Method)

u-Substitution Method (Cancelling Method)

  1. Find the integral \(\displaystyle\displaystyle \displaystyle\int 3x^{2} \sqrt{x^{3} + 5}\) \(dx\).
  2. Find the integral \(\displaystyle\displaystyle \displaystyle\int \frac{16x}{(4x^{2} + 4)^{2}}\) \(dx\).
  3. Evaluate the integral \(\displaystyle\displaystyle \displaystyle\int \frac{2x - 3}{\sqrt{x^{2} - 3x + 1}}\) \(dx\).
  4. Evaluate the integral \(\displaystyle\displaystyle \displaystyle\int -\frac{8x}{(2x^{2} + 3)^{2}}\) \(dx\).
  5. \(\displaystyle\displaystyle \displaystyle\int \frac{x}{x^{2} + 1}\) \(dx\)
  6. \(\displaystyle\displaystyle \displaystyle\int \frac{2x^{3}}{3x^{4} + 2}\) \(dx\)
  7. \(\displaystyle\displaystyle \displaystyle\int \sin 5x (2 - \cos 5x)^{5}\) \(dx\)
  8. \(\displaystyle\displaystyle \displaystyle\int \frac{\sin 2x}{3 - \cos 2x}\) \(dx\)

Video Solution:

Video Solution

Video solution locked

A free account saves your progress; this video needs a course plan.

Create free accountSign inGet the H2 Math course · from S$39.98/mo

Solution:

Solution locked

680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs a course plan.

Create free accountSign inGet the H2 Math course · from S$39.98/moH2 Math tuition

Create a free account to practise similar questions.

Create free accountSign inGet the H2 Math course · from S$39.98/moH2 Math tuition
Answer:Ex1: \(\displaystyle\frac{2}{3}(x^3+5)^{\frac{3}{2}} + C\); Ex2: \(-\displaystyle\frac{1}{2x^2+2} + C\); Ex3: \(2\sqrt{x^2-3x+1} + C\); Ex4: \(\displaystyle\frac{2}{2x^2+3} + C\); Ex5: \(\displaystyle\frac{1}{2}\ln|x^2+1| + C\); Ex6: \(\displaystyle\frac{1}{6}\ln|3x^4+2| + C\); Ex7: \(\displaystyle\frac{1}{30}(2-\cos 5x)^6 + C\); Ex8: \(\displaystyle\frac{1}{2}\ln|3-\cos 2x| + C\)

Need help? Join our JC Math tuition classes.

Learn more