 Hello and welcome to the session. The question says integrate the following function and the given function is root over 1-4x square. So first let us learn the formula to integrate the function of the type a square-x square with respect to x. This is equal to half to x into root over a square minus x square plus a square upon 2 to sin inverse x upon a plus c. So with the help of this formula we shall be integrating the given function. So this is our key idea. Now let us start with the solution. The given function is root over 1-4x square and this can further be written as 1 square minus 2x whole square. Now we have to integrate this function with respect to x. So we have integral root over 1 square minus 2x whole square into dx. Now let us put 2x is equal to t. So in differentiating both sides with respect to x we have 2 is equal to dt upon dx or dx is equal to dt upon 2. So this can further be written as integral root over 1 square minus t square into dt upon 2. Now taking the constant outside the integral sign we have half integral of root over 1 square minus t square into dt. Now I blank this formula this can further be written as half square bracket half into t root over 1 minus t square plus a square upon 2 that is 1 square upon 2 into sin inverse t upon 1 plus c where c is a constant. So this is further equal to 1 upon 4 substituting the value of t which is 2x into root over 1 minus 2x whole square is 4x square plus 1 upon 2 sin inverse 2x plus c or it can further written as sorry multiplying this half with this term also we get here 1 upon 2 also right. So this is further equal to first taking this term 1 upon 4 sin inverse 2x plus 2 cancels out with 4 and we get 1 upon 2 into x into root over 1 minus 4x square plus c. Thus on integrating the given function we get 1 upon 4 sin inverse 2x plus half into x into root over 1 minus 4x square plus c. So this completes the session by and take care.