Integration by substitution Quiz

1. Find $\int(3x-1)^4\,dx$ using $u=3x-1$.

• A. $\frac{(3x-1)^5}{15}+c$
• B. $\frac{(3x-1)^5}{5}+c$
• C. $\frac{3(3x-1)^5}{5}+c$
• D. $12(3x-1)^3+c$

2. In $\int x\sqrt{x-2}\,dx$ with $u=x-2$, what is $x$ in terms of $u$?

• A. $u-2$
• B. $u+2$
• C. $u$
• D. $2-u$

3. Using $u=x^2+3$, what are the new limits for $\int_0^1 2x(x^2+3)^4\,dx$?

• A. $0$ and $1$
• B. $1$ and $3$
• C. $4$ and $3$
• D. $3$ and $4$

4. Find $\int x\,e^{x^2}\,dx$ using $u=x^2$.

• A. $e^{x^2}+c$
• B. $2e^{x^2}+c$
• C. $\frac12e^{x^2}+c$
• D. $\frac12x^2e^{x^2}+c$

5. Evaluate $\int_0^2x(x^2+1)^3\,dx$ using $u=x^2+1$.

• A. $156$
• B. $78$
• C. $39$
• D. $624$