Question

The integral ${\int }_2^4\frac{log{x}^2}{log{x}^2+log(36-12x+x^2)}dx$ is equal to

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

Answer: (C)

$1$

$I={\int }_2^4\frac{2logx}{2logx+2log(6-x)}dx$

$I={\int }_2^4\frac{logx}{logx+log(6-x)}dx$

Using the property ${\int }_a^{b}f\left(x\right)dx={\int }_a^{b}f(a+b-x)dx$

we get,

$I={\int }_2^4\frac{log(6-x)}{logx+log(6-x)}dx$

Adding the two integrals we get,

$2I={\int }_2^{4}1dx$

Hence, $2I=2$

Hence, $I=1$