Integration Worksheet2 Solution3





In this page integration worksheet2 solution3 we are going to see solution of some practice question from the worksheet of integration.

Question 2

(i) Integrate the following with respect to x , 1/(x + 2)

Solution:

The given question exactly matches the formula 

∫ 1/(ax + b) dx = (1/a) log (a x + b) + c

Now we are going to integrate the given question by using this formula in the question instead of "a" we have 1

So we get,     

∫ 1/(x + 2) dx  = (1/1) log (x + 2) + C

                       =  log (x + 2) + C


(ii) Integrate the following with respect to x , 1/(3 x + 2)

Solution:

The given question exactly matches the formula 

∫ 1/(ax + b) dx = (1/a) log (a x + b) + c

Now we are going to integrate the given question by using this formula in the question instead of "a" we have 3

So we get,     

∫ 1/(3 x + 2) dx  = (1/3) log (3 x + 2) + C


(iii) Integrate the following with respect to x , 1/(3 - 4 x)

Solution:

The given question exactly matches the formula 

∫ 1/(ax + b) dx = (1/a) log (a x + b) + c

Now we are going to integrate the given question by using this formula in the question instead of "a" we have -4

So we get,     

∫ 1/(3 - 4 x) dx  = (-1/4) log (3 - 4 x) + C


(iv) Integrate the following with respect to x , 1/(p + q x)

Solution:

The given question exactly matches the formula 

∫ 1/(ax + b) dx = (1/a) log (a x + b) + c

Now we are going to integrate the given question by using this formula in the question instead of "a" we have q

So we get,     

∫ 1/(p + q x) dx  = (1/q) log (p + q x) + C


(iv) Integrate the following with respect to x , 1/(s - t x)

Solution:

The given question exactly matches the formula 

∫ 1/(ax + b) dx = (1/a) log (a x + b) + c

Now we are going to integrate the given question by using this formula in the question instead of "a" we have "-t"

So we get,     

∫ 1/(s - t x) dx  = (-1/t) log (s - t x) + C

integration worksheet2 solution3 integration worksheet2 solution3