Home
Class 12
MATHS
Evaluate the following integrals: int (x...

Evaluate the following integrals: `int (x^3 +3x +4)/sqrtx dx`

Text Solution

Verified by Experts

`int (x^3+3x+4)/sqrtx dx = int (x^3/sqrtx + (3x)/sqrtx + 4/sqrtx) dx`
=`int(x^(3-1/2) +3sqrtx+4/sqrtx)dx = int(x^(5/2) + 3x^(1/2) +4/sqrtx) dx`
=`x^(5/2+1)/(5/2+1) +3x^(1/2+1)/(1/2+1) + 4xx2sqrtx+c`
=`x^(7/2)/(7/2) +(3x^3/2))/(3/20 + 8sqrtx +c = (2x^(7/2)/7 + 2x^93/2) + 8sqrtx+c`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK |134 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|22 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following integrals: int_2^3 x^2 dx

Evaluate the following integrals: int_2^3 1/x dx

Evaluate the following integrals: int_4^5 e^x dx

Evaluate the following integrals int (2x^2 + e^x) dx

Evaluate the following integrals int (2x^2 - 3 sinx +5sqrtx) dx

Evaluate the following integrals: int(x^3 +5x^2 -4)/x^2 dx

Evaluate the following integrals int 1/(9x^2-1) dx

Evaluate the following integrals int (sqrtx - 1/sqrtx)^2 dx

Evaluate the following integrals int (1-x) sqrtx dx

Evaluate the following integrals int (x^3-x^2 +x -1)/(x-1) dx