Home
Class 12
MATHS
The anti derivative of (sqrt(x)+1/(sqrt(...

The anti derivative of `(sqrt(x)+1/(sqrt(x)))`equals(A) `1/3x^(1/3)+2x^(1/2)+C` (B) `2/3x^(2/3)+1/2x^2+C`(C) `2/3x^(3/2)+2x^(1/2)+C` (D) `3/2x^(3/2)+1/2x^(1/2)+C`

Text Solution

AI Generated Solution

To find the antiderivative of the function \( \sqrt{x} + \frac{1}{\sqrt{x}} \), we will integrate it step by step. ### Step 1: Rewrite the function We start by rewriting the function in terms of exponents: \[ \sqrt{x} = x^{1/2} \quad \text{and} \quad \frac{1}{\sqrt{x}} = x^{-1/2} \] Thus, we can express the function as: ...
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 7.8|6 Videos

  • INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 7.2|39 Videos

  • INTEGRALS

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|46 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT ENGLISH|Exercise EXERCISE 9.1|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT ENGLISH|Exercise Solved Examples|13 Videos

Similar Questions

Explore conceptually related problems

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

Evaluate int ((8x+13)/sqrt(4x+7)) dx (A) 1/3 (4x+7)^(3/2) - 1/2 (4x+7)^(1/2) + c (B) 1/6 (4x+7)^(5/2) - 2/3 (4x+7)^(3/2) + c (C) 1/3 (4x+7)^(5/2) - 1/2 (4x+7)^(3/2) + c (D) (4x+7)^(3/2) - 1/2 (4x+7)^(1/2) + c

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

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))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

The derivative of sec^(-1)(1/(2x^2-1)) with respect to sqrt(1+3x) at x=-1/3 (a) does not exist (b) 0 (c) 1/2 (d) 1/3

The value of x=sqrt(2+sqrt(2+sqrt(2+...))) is (a) -1 (b) 1 (c) 2 (d) 3

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)

If int((x+1))/sqrt(2x-1) dx= f(x) sqrt(2x-1)+C. Then f(x) is equal to (A) (x+4)/3 (B) (x+3)/4 (C) 2/3 (x+2) (D) x+4