(1)/((2x-7)sqrt((x-3)(x-4)))

If int (dx)/((2x-7) sqrt((x-3) (x-4))) = 1/k sec^(-1) (2x-7)+ c , then the value of k is -

(27^(((1)/(5)))((x)/(4)-sqrt((x)/(3))))^((x)/(4)+sqrt((x)/(3)))=3^((7)/(4))

Choose the correct answer int sqrt(x^(2)-8x+7)dx(A)(1)/(2)(x-4)sqrt(x^(2)-8x+7)+9log|x-4+sqrt(x^(2)-8x+7)|+C(1)/(2)(x+4)sqrt(x^(2)-8x+7)+9log|x+4+sqrt(x^(2)-8x+7)|+C(C)(1)/(2)(x-4)sqrt(x^(2)-8x+7)-3sqrt(2)log|x-4+sqrt(x^(2)-8x+7)|+(1)/(2)(x-4)sqrt(x^(2)-8x+7)-((9)/(2))log|x-4+sqrt(x^(2)-8x+7)|

Prove that the following equations has no solutions. (i) sqrt((2x+7))+sqrt((x+4))=0 (ii) sqrt((x-4))=-5 (iii) sqrt((6-x))-sqrt((x-8))=2 (iv) sqrt(-2-x)=root(5)((x-7)) (v) sqrt(x)+sqrt((x+16))=3 (vi) 7sqrt(x)+8sqrt(-x)+15/(x^(3))=98 (vii) sqrt((x-3))-sqrt(x+9)=sqrt((x-1))

Solve for x:sqrt(2x-1)+sqrt(3x-2)=sqrt(4x-3)+sqrt(5x-4)

If Delta (x) =|{:(4x-4,(x-2)^(2),x^(3)),(8x-4sqrt(2),(x-2sqrt(2)^(2)),(x+1)^(3)),(12x-4sqrt(3),(x-2sqrt(3))^(2),(x-1)^(3)):}| then

If Delta (x) =|{:(4x-4,(x-2)^(2),x^(3)),(8x-4sqrt(2),(x-2sqrt(2)^(2)),(x+1)^(3)),(12x-4sqrt(3),(x-2sqrt(3))^(2),(x-1)^(3)):}| then

int_(-(1)/(sqrt(3)))^(-(1)/(sqrt(3)))(x^(4))/(1-x^(4))cos^(-1)((2x)/(1+x^(2)))dx

If x=(1)/(2)(sqrt(7)+(1)/(sqrt(7))) ,then , log_(27)((sqrt(x^(2)-1))/(x-sqrt(x^(2)-1))) is equal to