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" 21."log sqrt((1+cos^(2)x)/(1-e^(2x)))q...

" 21."log sqrt((1+cos^(2)x)/(1-e^(2x)))quad ("C.B.S.E."2003C)

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Find the integral int(1)/(5-8x-x^(2))dx A. (1)/(2sqrt(21))log|(sqrt(21)+(x+4))/(sqrt(21)-(x+4))|+C .B. (1)/(2sqrt(21))log|(sqrt(21)-(x+4))/(sqrt(21)+(x+4))|+C C. (1)/(sqrt(21))log|((x+4)+sqrt(21))/((x+4)-sqrt(21))|+Cquad D. (1)/(sqrt(21))log|((x+4)-sqrt(21))/((x+4)+sqrt(21))|+C

Column I, a) int(e^(2x)-1)/(e^(2x)+1)dx is equal to b) int1/((e^x+e^(-x))^2)dx is equal to c) int(e^(-x))/(1+e^x)dx is equal to d) int1/(sqrt(1-e^(2x)))dx is equal to COLUMN II p) x-log[1+sqrt(1-e^(2x)]+c q) log(e^x+1)-x-e^(-x)+c r) log(e^(2x)+1)-x+c s) -1/(2(e^(2x)+1))+c

Column I, a) int(e^(2x)-1)/(e^(2x)+1)dx is equal to b) int1/((e^x+e^(-x))^2)dx is equal to c) int(e^(-x))/(1+e^x)dx is equal to d) int1/(sqrt(1-e^(2x)))dx is equal to COLUMN II p) x-log[1+sqrt(1-e^(2x)]+c q) log(e^x+1)-x-e^(-x)+c r) log(e^(2x)+1)-x+c s) -1/(2(e^(2x)+1))+c

Column I, a) int(e^(2x)-1)/(e^(2x)+1)dx is equal to b) int1/((e^x+e^(-x))^2)dx is equal to c) int(e^(-x))/(1+e^x)dx is equal to d) int1/(sqrt(1-e^(2x)))dx is equal to COLUMN II p) x-log[1+sqrt(1-e^(2x)]+c q) log(e^x+1)-x-e^(-x)+c r) log(e^(2x)+1)-x+c s) -1/(2(e^(2x)+1))+c

Column I, a) int(e^(2x)-1)/(e^(2x)+1)dx is equal to b) int1/((e^x+e^(-x))^2)dx is equal to c) int(e^(-x))/(1+e^x)dx is equal to d) int1/(sqrt(1-e^(2x)))dx is equal to COLUMN II p) x-log[1+sqrt(1-e^(2x)]+c q) log(e^x+1)-x-e^(-x)+c r) log(e^(2x)+1)-x+c s) -1/(2(e^(2x)+1))+c

int(dx)/(x-sqrt(x)) is equal to a) 2log|sqrt(x)-1|+C b) 2log|sqrt(x)+1|+C c) log|sqrt(x)-1|+C d) (1)/(2)log|sqrt(x)+1|+C