Integration By Substitution

Step 1: Use substitution.
Let $u%20%3D%20x%5E%7B10%7D$ . Then, $%5Cfrac%7Bdu%7D%7Bdx%7D%20%3D%2010x%5E9%20%5C(%5CRightarrow%5C)%20dx%20%3D%20%5Cfrac%7Bdu%7D%7B10x%5E9%7D$

Step 2: Rewrite the integral.
Substituting into the integral: $%5Cint%20x%5E9%20%5Ccdot%20%5Csec%5E2(x%5E%7B10%7D)%20%5C%2C%20dx%20%3D%20%5Cint%20%5Csec%5E2(u)%20%5Ccdot%20%5Cfrac%7Bdu%7D%7B10%7D$ $%3D%20%5Cfrac%7B1%7D%7B10%7D%20%5Cint%20%5Csec%5E2(u)%20%5C%2C%20du$

Step 3: Integrate.
The integral of $%5Csec%5E2(u)$ is $%5Ctan(u)$ , so: $%5Cfrac%7B1%7D%7B10%7D%20%5Cint%20%5Csec%5E2(u)%20%5C%2C%20du%20%3D%20%5Cfrac%7B1%7D%7B10%7D%20%5Ctan(u)%20%2B%20C$

Step 4: Substitute back for $u$ .
Since $u%20%3D%20x%5E%7B10%7D$ , the final answer is: $%5Cfrac%7B1%7D%7B10%7D%20%5Ctan(x%5E%7B10%7D)%20%2B%20C$

Final Answer: $%5Cboxed%7B%5Cfrac%7B1%7D%7B10%7D%20%5Ctan(x%5E%7B10%7D)%20%2B%20C%7D$

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Integration By Substitution

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs