U-Sub Integration + Special Rules

∫ 5e^5x dx

• 25 e^5x + C

• 5 e^{5x - 1} + C

• e^5x + C

• (1/5) e^5x + C

• ln(2x²+6) + C
• ln(2x²+6)(4x) + C
• 1/(2x²+6) + C
• 1/(2x²+6)² + C

Do you use u substitution to integrate this? $\int\left(3x-4\right)^4dx$  

• Yes

• No

• Yes

• No

What should be assigned to u in the integral?

• 2x²

• sin(2x²)

• 5x

• no u needed

What is  $\int_{\ }^{\ }4\cdot3^{2x}dx$  ?

•  $\frac{2\cdot3^{2x}}{\ln\left|3\right|}+C$  

•  $\frac{3^{2x}}{\ln\left|3\right|}+C$  

•  $8e^{2x}+C$  

•  $2\ln\left|2x\right|+C$  

What is  $\int_{\ }^{\ }9x^2e^{\left(3x^3-5\right)}\ dx$  

•  $\ln\left|3x^3-5\right|+C$  

•  $e^{\left(3x^3-5\right)}+C$  

•  $\frac{3^{\left(3x^3-5\right)}}{\ln\left|3\right|}+C$  

•  $2e^{\left(3x^3-5\right)}+C$  

What is  $\int_{\ }^{\ }-x\cdot4^{\left(x^2+2\right)}dx$  

•  $e^{\left(x^2+2\right)}+C$  

•  $4^{\left(x^2+2\right)}+C$  

•  $-\frac{1}{2}\ln\left|x^2+1\right|+C$  

•  $-\frac{4^{\left(x^2+2\right)}}{2\ln\left|4\right|}+C$  

What is  $\int_{\ }^{\ }\frac{40x}{5x^2+1}dx$  

•  $\frac{4\cdot3^{\left(5x^2+1\right)}}{\ln\left|3\right|}+C$  

•  $4\ln\left|5x^2+1\right|+C$  

•  $e^{\left(5x^2+1\right)}+C$  

•  $\ln\left|5x^2+1\right|+C$  

 $\int_{\ }^{\ }6x\cot\left(3x^2+5\right)dx$  

•  $\tan\left(3x^2+5\right)+C$  

•  $\ln\left|\sin\left(3x^2+5\right)\right|+C$  

•  $\sec\left(3x^2+5\right)+C$  

•  $\ln\left|\cos\left(3x^2+5\right)\right|+C$