`int_(-1)^1 (x^3 + |x| + 1)/(x^2 + 2|x| + 1) \ dx` is (i) `log2` (ii) `2log2` (iii) `1/2log(2)` (iv) `4log2`

int_(1)^(e )(1)/(6x(log x)^(2)+7x log x + 2x)dx=

int_(0tooo) log(1+x^2)/(1+x^2) dx equals-(A) log2(B) -a log2(C) 1/2 log2(D) -A/2 log2

int_(-1)^(1)(x^(3)+|x|+1)/(x^(2)+2|x|+1)dx , is equal to a) ln2 b) 2 ln 2 c) 1/2 ln 2 d)None of these

I=int_(-1)^(1)log((2-x)/(2+x))dx

int_((1)/(2))^(2)(ln x)/(1+x^(2))dx

(i) int x^2 log x dx (ii) int (x^2+1) log x dx

Solve for x : (i) log_(10) (x - 10) = 1 (ii) log (x^(2) - 21) = 2 (iii) log(x - 2) + log(x + 2) = log 5 (iv) log(x + 5) + log(x - 5) = 4 log 2 + 2 log 3

If log_(10)(2),log_(10)(2^(x)+1),log_(10)(2^(x)-3) are in A.P then x is equal to (i)log_(2)(5)( ii) log_(2)(-1) (iii) log_(2)((1)/(5))( iv) log_(5)(2)

The value of int_(0)^(1)(8log(1+x))/(1+x^(2))dx is: (1)pi log2 (2) (pi)/(8)log2(3)(pi)/(2)log2(4)log2