In this page integration worksheet2 solution5 we are going to see
solution of some practice question from the worksheet of integration.

**Question 5**

(i) Integrate the following with respect to x ,sec² (2 - x)

**Solution:**

The given question exactly matches the formula

**∫**** sec² (a x + b) = (1/a) tan ****(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,

∫ sec² (2 - x) dx = (1/-1) tan (2 - x) + C

= - tan (2 - x) + C

(ii) Integrate the following with respect to x ,cosec² (5 + 2 x)

**Solution:**

The given question exactly matches the formula

**∫**** cosec² (a x + b) = -(1/a) cot ****(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 2

So we get,

∫ cosec² (5 + 2 x) dx = -(1/2) cot (5 + 2 x) + C

= - cot (5 + 2 x)/2 + C

(iii) Integrate the following with respect to x ,Sec² (3 + 4 x)

**Solution:**

The given question exactly matches the formula

**∫**** sec² (a x + b) = (1/a) tan ****(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,

∫ Sec² (3 + 4 x) dx = (1/4) tan (3 + 4 x) + C

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

(iv) Integrate the following with respect to x , cosec² (7 - 11 x)

**Solution:**

The given question exactly matches the formula

**∫**** cosec² (a x + b) = - (1/a) cot ****(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 -11

So we get,

∫ cosec² (7 - 11 x) dx = -(1/-11) cot (7 - 11 x) + C

= cot (7 - 11 x)/11 + C

(v) Integrate the following with respect to x ,sec² (p - q x)

**Solution:**

The given question exactly matches the formula

**∫**** sec² (a x + b) = (1/a) tan ****(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,

∫ sec² (p - q x) dx = (1/-q) tan (p - q x) + C

= - tan (p - q x)/q + C

integration worksheet2 solution5 integration worksheet2 solution5

- 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