# GSEB Solutions Class 12 Maths Chapter 7 Integrals Ex 7.3

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.3 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.3

Find the integrals of the following:
Question 1.
sin2(2x + 5)
Solution:

Question 2.
sin3x cos4x
Solution:

Question 3.
cos2x cos4x cos6x
Solution:

Question 4.
sin3(2x + 1)
Solution:

Question 5.
sin3x cos3x
Solution:

Question 6.
sinx sin2x sin3x
Solution:

Question 7.
sin4x sin8x
Solution:

Question 8.
$$\frac{1-cosx}{1+cosx}$$
Solution:

Question 9.
$$\frac{cosx}{1+cosx}$$
Solution:

Question 10.
sin4x
Solution:

Question 11.
cos42x
Solution:

Question 12.
$$\frac{\sin ^{2} x}{1+\cos x}$$
Solution:

= x – sinx + C.

Question 13.
$$\frac{cos2x-cos2Î±}{cosx-cosÎ±}$$
Solution:

Question 14.
$$\frac{cosx-sinx}{1+sin2x}$$
Solution:

Question 15.
tan32x sec2x
Solution:

Question 16.
tan4x
Solution:

Question 17.
$$\frac{\sin ^{3} x+\cos ^{3} x}{\sin ^{2} x \cos ^{2} x}$$
Solution:

Question 18.
$$\frac{\cos 2 x+2 \sin ^{2} x}{\cos ^{2} x}$$
Solution:

Question 19.
$$\frac{1}{\sin x \cos ^{3} x}$$
Solution:

Question 20.
$$\frac{\cos 2 x}{(\cos x+\sin x)^{2}}$$
Solution:

Question 21.
sin-1x
Solution:

Question 22.
$$\frac{1}{cos(x-a)cos(x-b)}$$
Solution:

Choose the correct answers in the following questions 23 and 24:
Question 23.
âˆ« $$\frac{\sin ^{2} x-\cos ^{2} x}{\sin ^{2} x \cos ^{2} x}$$
(A) tan x + cot x + C
(B) tan x + cosec x + C
(C) – tan x + cot x + C
(D) tan x + sec x + C
Solution:

âˆ´ part (A) is the correct answer.

Question 24.
âˆ« $$\frac{e^{x}(1+x)}{\cos ^{2}\left(x e^{x}\right)}$$ is equal to.
(A) – cot (e.xx)
(B) tan (x.ex) + C
(C) tan (ex) + C
(D) cot (ex) + C
Solution:
I = âˆ« $$\frac{e^{x}(1+x)}{\cos ^{2}\left(x e^{x}\right)}$$ dx.
Put x ex = t, so that (ex + x ex) dx = dt.
or ex(1 + x)dx = dt
âˆ´ I = âˆ« $$\frac{d t}{\cos ^{2} t}$$ = âˆ«sec2 t dt = tan t + C.
= tan(x ex) + C.
âˆ´ Part (B) is the correct answer.