Question 1.
Solution:
Given integral,
On Multiplying and dividing with 2, we get
⇒
⇒
⇒
⇒
By using the formula,
[where c is any arbitrary constant] We get
⇒
⇒
⇒
⇒
Question 2.
Solution:
Given integral,
Let x + 2 =t ⇒ x = t – 2
On differentiating on both sides,
dx = dt
On substituting it in given integral, we get
⇒
⇒
We know that,
[where c is any arbitrary constant] ⇒
⇒
Replacing x in terms of t
⇒
⇒
Question 3.
Solution:
Given integral,
⇒
⇒
⇒
By using the formula,
[where c is any arbitrary constant] We get
⇒
⇒
⇒
Question 4.
Solution:
Given integral,
Let 3x + 5 = t
⇒ x = (t – 5)/3
On differentiating both sides,
dx = dt/3
On replacing the x terms with t,
⇒
⇒
⇒
By using the formula,
[where c is any arbitrary constant] We get
⇒
⇒
On replacing t with x terms
⇒
⇒
⇒
Question 5.
Solution:
Given integral,
On multiplying and dividing it with 3
⇒
⇒
⇒
⇒
By using the formula,
[where c is any arbitrary constant] We get
⇒
⇒
⇒
⇒
⇒
Question 6.
Solution:
Given integral,
Let 7x + 9 = t
⇒ x = (t – 9)/7
On differentiating both sides,
dx = dt/7
On replacing x terms with t
⇒
⇒
⇒
By using the formula,
[where c is any arbitrary constant] ⇒
⇒
On replacing t with x terms
⇒
⇒
Question 7.
Solution:
Given integral,
⇒
⇒
By using the formula,
[where c is any arbitrary constant] ⇒
⇒
⇒
Question 8.
Solution:
Given integral,
Let 1 + 3x = t
⇒ x = (t – 1)/3
On differentiating both sides, we get
dx = dt/3
On replacing x with t
⇒
⇒
⇒
By using the formula,
[where c is any arbitrary constant] ⇒
Now on replacing t in terms of x
⇒
⇒
⇒
Question 9.
Solution:
Given integral,
Let 2x – 1 = t2
⇒ x = (t2 + 1)/2
On differentiating on both sides,
dx = tdt
⇒
⇒
⇒
By using the formula,
[where c is any arbitrary constant] ⇒
On replacing t with x terms
⇒
⇒
⇒
⇒
Question 10.
Solution:
Given integral,
On multiplying and dividing the given integral with
We know that (a + b)(a – b) = a2 – b2
⇒
⇒
⇒
⇒
By using the formula,
[where c is any arbitrary constant] ⇒
⇒