Problem:

$\displaystyle \int\frac{1}{11+x^2}dx$

Attempt:

$\displaystyle \int\frac{1}{11+(\sqrt{11}+tan(\theta))^2} * \frac{\sqrt{11} *d\theta}{cos^2\theta}$$\displaystyle x = \sqrt{11}*tan(\theta)$

$\displaystyle dx = \frac{\sqrt{11} *d\theta}{cos^2\theta}$

$\displaystyle \int\frac{\sqrt{11}*d\theta}{(11+\sqrt{11}*tan(\th eta))^2*cos^2(\theta)}$

$\displaystyle \int\frac{\sqrt{11}*d\theta}{(11+11*tan^2(\theta)) *cos^2(\theta)}$

$\displaystyle

\int\frac{\sqrt{11}*d\theta}{11(1+\frac{sin^2(\the ta)}{cos^2(\theta})*cos^2(\theta)}

$

$\displaystyle

\int\frac{\sqrt{11}*d\theta}{11*(cos^2(\theta)+sin ^2(\theta))}

$

$\displaystyle

\int\frac{\sqrt{11}*d\theta}{11}

$

$\displaystyle

\frac{\sqrt{11}*\theta}{11} + C

$

Answer:

$\displaystyle \frac{\sqrt{11}}{11}*arctan(\frac{x}{\sqrt{11}})+C$

Correct Answer:

$\displaystyle \frac{1}{\sqrt{11}}*arctan(\frac{x}{\sqrt{11}})+C$

Can someone help?