# Class 12 RD Sharma Solutions – Chapter 19 Indefinite Integrals – Exercise 19.28

### Question 1. Find

Solution:

Let considered x – 1 = t,

so that dx = dt

Thus,

Solution:

Let I =

Solution:

I =

Hence,

Solution:

Let I =

Therefore, I =

### Question 5.

Solution:

I =

Let us considered sinx = t

So, on differentiating, we get

cosx dx = dt

I =

Therefore, I =

### Question 6. Evaluate

Solution:

I =

Let us considered ex = t

So, on differentiating, we get

exdx = dt

Therefore, I =

Hence, I =

Solution:

I =

Therefore, I =

### Question 8. Evaluate

Solution:

Let us assume I =

Therefore, I =

### Question 9. Evaluate

Solution:

Let us assume I =

Therefore, I =

### Question 10. Evaluate

Solution:

Let us assume I =

Therefore, I =

### Question 11. Evaluate

Solution:

Let us assume I =

Therefore, I =

### Question 12. Evaluate

Solution:

Let us assume x2 = t

On differentiating we get

2x dx = dt

Therefore, I =

Hence, I =

### Question 13. Evaluate

Solution:

I =

Let us considered x3 = t

So, on differentiating, we get

3x2dx = dt

Therefore, I =

Hence, I =

### Question 14. Evaluate

Solution:

I =

Let us considered logx = t

So, on differentiating, we get

1/x dx = dt

Therefore, I =

Hence, I =

Solution:

I =

Therefore, I =

Solution:

Let I =

I =

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