Integration

If y = $ax^n$  , then  $\int_{ }^{ }y\ dx\ =$  

•  $\frac{ax^{n+1}}{n+1}$  

•  $\frac{ax^{n-1}}{n-1}+\ c$  
  

•  $\frac{ax^{n+1}}{n}+\ c$  

•  $\frac{ax^{n+1}}{n+1}+\ c$  

Which of the following is the indefinite integral of  $\frac{x^3}{2}+7$  ?

•  $\frac{3x^2}{2}$  

•  $\frac{3x^2}{2}+7x+c$  

•  $\frac{x^4}{8}+7x+c$  

•  $\frac{x^4}{8}+c$  

Integrate  $\sqrt{x}$  with respect to x

•  $x^{\frac{1}{2}}+c$  

•  $\frac{1}{2}x^{-\frac{1}{2}}+\ c$  

•  $\frac{2}{3}x^{\frac{3}{2}}+\ c$  

•  $\frac{3}{2}x^{\frac{3}{2}}+\ c$  

Which of the following is the indefinite integral of  $\frac{3}{x^4}\ \ ?$ 

•  $-\frac{1}{x^3}+\ c$  

•  $\frac{3}{5x^5}+\ c$  
  

•  $-\frac{12}{x^5}+\ c$  

•  $\frac{1}{x^3}+\ c$  

Integrate  $\int\left(2x+1\right)^{10}\ dx$  with respect to x.

•  $22\left(2x+1\right)^{11}+c$  

•  $\frac{1}{22}\left(2x+1\right)^{11}+c$  

•  $11\left(2x+1\right)^{10}+c$  

•  $\frac{1}{11}\left(2x+1\right)^{10}+c$  

 $\int_{ }^{ }e^{5x}dx\ =$  

•  $e^{5x}+c$  

•  $5e^{5x}+c$  

•  $\frac{1}{5}e^{5x}+c$  

• none of these

 $\int\ \frac{2}{x+3}dx^{ }=$  

• 2ln|x+3| + c

• 2ln(x + 3) + c

•  $\frac{1}{2}\ln\left|x\ +\ 3\right|\ +\ c$  

• none of these

∫ 2x cos(x²) dx

• sin(x²) + C

• 2 sin ( 2x ) + C

• (1/2) sin(x²) + C

• 4 cos(2x ) + C

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

∫ 2x cos(x²) dx

• sin(2x) + C
• 2 sin ( 2x ) + C 
• (1/2) sin(2x) + C 
• 4 cos(2x ) + C