Home
Class 12
MATHS
Choose the correct answer intsqrt(a+x^2)...

Choose the correct answer `intsqrt(a+x^2)dx` is equal to (A) `x/2sqrt(1+x^2)+1/2log|(x+sqrt(x+x^2))|+C` (B) `2/3(1+x^2)^(3/2)+C` (C) `2/3x(1+x^2)^(3/2)+C` (D) `(x^2)/2sqrt(1+x^2)+1/2x^2log|x+sqrt(1+x^2)|+C`

Text Solution

Verified by Experts

The correct Answer is:
A
`" Let I "= int sqrt(1+x^(2))dx`
` rArr I =(x)/(2) sqrt(1+x^(2))+(1)/(2)log |x+sqrt(1+x^(2))|+c`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.8|6 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.9|22 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.6|24 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise (prove That )|9 Videos

Similar Questions

Explore conceptually related problems

Choose the correct answer intsqrt(1+x^2)dx is equal to(A) x/2sqrt(1+x^2)+1/2log|(x+sqrt(x+x^2))|+C (B) 2/3(1+x^2)^(3/2)+C (C) 2/3x(1+x^2)^(3/2)+C (D) (x^2)/2sqrt(1+x^2)+1/2x^2log|x+sqrt(1+x^2)|+C

int(x^3dx)/(sqrt(1+x^2)) is equal to (A) 1/3sqrt(1+x^2)(2+x^2)+C (B) 1/3sqrt(1+x^2)(x^2-1)+C (C) 1/3(1+x^2)^(3/2)+C (D) 1/3sqrt(1+x^2)(x^2-2)+C

int(x^3dx)/(sqrt(1+x^2))i se q u a lto 1/3sqrt(1+x^2)(2+x^2)+C 1/3sqrt(1+x^2)(x^2-1)+C 1/3(1+x^2)^(3/2)+C (d) 1/3sqrt(1+x^2)(x^2-2)+C

Choose the correct answer intx^2e^x^3dx equals (A) 1/3e^x^3+C (B) 1/3e^x^2+C (C) 1/2e^x^3+C (D) 1/2e^x^2+C

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

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

Choose the correct answer intx^2e^(x^3)dx equals(A) 1/3e^(x^3) +C (B) 1/3e^(x^2)+C (C) 1/2e^(x^3)+C (D) 1/2e^(x^2)+C

int 1/ sqrt (a^2 + x^2) dx = log ( x + sqrt(x^2 + a^2)) + c

"tan"(cos^(-1)x) is equal to x/(1+x^2) b. (sqrt(1+x^2))/x c. (sqrt(1-x^2))/x d. sqrt(1-2x)

The value of sin(cot^-1x)= (A) sqrt(1+x^2) (B) x (C) (1+x^2)^(-3/2) (D) (1+x^2)^(-1/2)