Indefinite Integrals Maths - Indefinite Integrals

1. $\frac{1}{2}\log\big(\sec\text{x}^2+\tan\text{x}^2\big)+\text{C}$
   
2. $\frac{\text{x}^2}{2}\log\big(\sec\text{x}^2+\tan\text{x}^2\big)+\text{C}$
   
3. $2\log\big(\sec\text{x}^2+\tan\text{x}^2\big)+\text{C}$
   
4. none of these.
   

1. $1+\log\text{x}$
   
2. $\text{x}+\log\text{x}$
   
3. $\text{x}\log\text{x}(1+\log\text{x})$
   
4. $\log(1+\log\text{x})$
   

1. $\frac{\text{e}^\text{x}}{\text{x}+4}+\text{C}$
   
2. $\frac{\text{e}^\text{x}}{\text{x}+3}+\text{C}$
   
3. $\frac{1}{(\text{x}+4)^2}+\text{C}$
   
4. $\frac{\text{e}^\text{x}}{(\text{x}+4)^2}+\text{C}$
   

1. $\log\big|1+\cot\frac{\pi}{2}\big|+\text{C}$
   
2. $\log\big|1-\tan\frac{\pi}{2}\big|+\text{C}$
   
3. $\log\big|1-\cot\frac{\pi}{2}\big|+\text{C}$
   
4. $\log\big|1+\tan\frac{\pi}{2}\big|+\text{C}$
   

1. $\text{a}=-\frac{1}{10},\text{ b}=\frac{2}{5}$
   
2. $\text{a}=\frac{1}{10},\text{ b}=\frac{2}{5}$
   
3. $\text{a}=-\frac{1}{10},\text{ b}=\frac{2}{5}$
   
4. $\text{a}=\frac{1}{10},\text{ b}=\frac{2}{5}$
   

$\int\frac{\text{e}^\text{x}}{1+\text{e}^{2\text{x}}}\text{dx}$

$\int\frac{\text{x}+\sin\text{x}}{1+\cos\text{x}}\text{dx}$

$\int\frac{\log(\text{x}+2)}{(\text{x}+2)^2}\text{dx}$

$\int\sin^{-1}\sqrt{\text{x}}\text{dx}$

$\int\frac{\text{x}}{\text{x}^2+3\text{x}+2}\text{ dx}$

$\int(\log\text{x})^2\cdot\text{x dx}$

$\int\text{x}^2\sin^{-1}\text{x dx}$

$\int\sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)\text{dx}$