In this page integration worksheet2 solution6 we are going to see
solution of some practice question from the worksheet of integration.

**Question 6**

(i) Integrate the following with respect to x , sec (3 + x) tan (3 + x)

**Solution:**

The given question exactly matches the formula

**∫sec (a x + b) tan (a x +b) = (1/a) sec (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,

∫ sec (3 + x) tan (3 + x) dx = (1/1) sec (3 -x) + C

= sec (3 - x) + C

(ii) Integrate the following with respect to x , sec (3 x + 4) tan (3 x + 4)

**Solution:**

The given question exactly matches the formula

**∫sec (a x + b) tan (a x +b) = (1/a) sec (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,

∫ sec (3 x + 4) tan (3 x + 4) dx = (1/3) sec (3 x + 4) + C

= sec (3 x + 4)/3 + C

(iii) Integrate the following with respect to x , sec (4 - x) tan (4 - x)

**Solution:**

The given question exactly matches the formula

**∫sec (a x + b) tan (a x +b) = (1/a) sec (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,

∫ sec (4 - x) tan (4 - x) dx = (1/-1) sec (4 - x) + C

= - sec (4 - x) + C

(iv) Integrate the following with respect to x , sec (4 - 3 x) tan (4 - 3 x)

**Solution:**

The given question exactly matches the formula

**∫sec (a x + b) tan (a x +b) = (1/a) sec (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,

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

= - sec (4 - 3 x)/3 + C

(v) Integrate the following with respect to x , sec (a x + b) tan (a x + b)

**Solution:**

The given question exactly matches the formula

**∫sec (a x + b) tan (a x +b) = (1/a) sec (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

So we get,

∫sec (a x + b) tan (a x + b) dx = (1/a) sec (a x + b) + C

integration worksheet2 solution6 integration worksheet2 solution6

- Back to worksheet
- 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