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

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- Integration
- Substitution method
- Decomposition method
- Properties of integrals
- Integration-by parts
- Integration-of Sec³ x
- Standard integrals
- Integrating quadratic denominator
- Integration-using partial fractions
- Definite integrals