JEE Advanced · 2006 · 09 Apr 2006 · Indefinite Integrals

More JEE Advanced questions on Indefinite Integrals

1. If
   

   $$\alpha ={\int }_0^1\left(e^{9x+3{\tan }^{-1}x}\right)\left(\frac{12+9x^2}{1+x^2}\right)dx$$

   
   where ${\tan }^{-1}x$ takes only principal values, then the value of $\left({\log }_e|1+\alpha |-\frac{3\pi }{4}\right)$ is
   JEE Advanced 2015 Copy linkView solution →
2. The value of
   

   $${\int }_0^{1}4x^3\left\{\frac{d^2}{d{x}^2}{\left(1-x^2\right)}^5\right\}dx$$

   
   is
   JEE Advanced 2014 Copy linkView solution →
3. The integral $\int \frac{{\sec }^{2}x}{(\sec x+\tan x{)}^{9/2}}dx$ equals (for some arbitrary constant $K$ )
   JEE Advanced 2012 Copy linkView solution →
4. Let
   

   $$I=\int \frac{e^x}{e^{4x}+e^{2x}+1}dx,J=\int \frac{e^{-x}}{e^{-4x}+e^{-2x}+1}dx$$

   
   Then, for an arbitrary constant $C$, the value of $J-I$ equals
   JEE Advanced 2008 Copy linkView solution →
5. Let $F(x)$ be an indefinite integral of ${\sin }^{2}x$.
   
   STATEMENT-1 : The function $F(x)$ satisfies $F(x+\pi )=F(x)$ for all real $x$.
   
   because
   
   STATEMENT-2 : ${\sin }^2(x+\pi )={\sin }^{2}x$ for all real $x$.
   JEE Advanced 2007 Copy linkView solution →
6. Let $f(x)=\frac{x}{{\left(1+x^n\right)}^{1/n}}$ for $n\ge 2$ and $g(x)=\underset{f\text{ occurs }n\text{ times }}{\underbrace{(f\circ f\circ \cdots \circ f)}}(x)$. Then $\int x^{n-2}g(x)dx$ equals
   JEE Advanced 2007 Copy linkView solution →