18 If csc(x) (in Quadrant-I), find 7 = s(2x)% = COS %3D

Q: Evaluate

A: ∫3cos22x dx factor out the constant term outside integral symbol. ∫3cos22xdx =3∫1cos22xdx=3∫sec22xdx…

Q: 7. S tan 5x dx

A: Using integration

Q: х cos 2x dx

A: First apply u-substitution, u=2x. Thus integration becomes,

Q: vi. ſ cos(3 Inx)dx

A: Using definite integrals,

Q: S cos32x dx.

A:

Q: Evaluate fea cos(2x) dx

A: We have to above integration

Q: 78 |x cos(nx)dx

A: As per guidelines we will solve one question

Q: 1 36* dx V6* + 3

A: We have to find

Q: 14. S4 cos (-3x + 2) dx

A:

Q: cos(15x) cos(4r) dx

A: Given∫cos(15x)cos(4x)dx  ...(1)For the simplification apply the trigonometric identitycos(a…

Q: c- S cos(Inx).dx

A:

Q: S cos 4x cos 3x dx

A: We need to evaluate integral.

Q: 7. S (x-1+cosx) cos2(sinx+lnx)

A: We use substitution method to solve this integration

Q: Evaluate fe.cos 2x dx

A: ∫e3x cos2x dx

Q: 12, S a cos Vx dx COS

A:

Q: [(1+cos 3x) dx 3x)?dx + cos

A: Given: I=∫(1+cos(3x))32dx

Q: S sin5x cos³x dx

A: Given∫sin5xcos3xdx

Q: х cos(5x) dx —

A:

Q: Find integral.

A: Consider the indefinite integral ∫-6x cos 5x dx Use the integration by parts to solve the indefinite…

Q: 6. cos-1 Vx dx

A:

Q: 1 dx 6- cos²xsin²x

A: use trigonometric identity to prove the integral

Q: Cos^3(3x) dx

A:

Q: S cos 2x dx COSX

A:

Q: S 1+cos(3x)dx

A: Given : ∫1+cos3xdx

Q: S cos(7x) cos (18x)dx

A:

Q: fxcos (x)dx COS

A: Assume u=x^2Find du

Q: S cos" (3x) dx CoS

A: Apply integration by parts

Q: 4. COS dx sin?

A:

Q: )S sin cos5 x dx

A: Solve the following integral

Q: O cos 4x + (Dx + E) C) cos 4x + (Dx+ Am Cm 2:

A:

Q: 3) cos-1x. dx

A:

Q: x5-3 14. S4 cos (-3x + 2) dx

A:

Q: cos'x sm'e dx

A:

Q: d. cos 3x = 0 e. tan 4x - 1 = 0

A: Given:- d.  cos(3x) =0  e. tan(4x) -1=0 To find:- Solution of given equations

Q: S cos²(2x)dx

A:

Q: ∫cos^4 2x dx

A: Please see the answer in step 2

Q: cos (In4x2) dx

A: Topic:- integration

Q: S tan-1(bx) dx

A:

Q: QUESTION 2 Find % for the equation y = cosh (2x)tanh x - %3D dx

A:

Q: 24 dx 1- cos (6x)

A:

Q: 50 6x sin dx e sec sec

A: The question seems to be wrong. I have made a few changes. The solution is as follows below:

Q: ∫(π/2) cosx dx 0

A:

Q: 7 dx = x3

A: ∫xndx=xn+1n+1+C1xn=x-n

Q: -3x cos (5x)dx

A:

Q: S cos 8x dx

A:

Q: (1) S cos(7x + 5)dx

A: We need to integrate the given terms.  For this we will use substitution method.

Q: cos(3x + 2) dx

A: This is based on simple integral formula

Q: S cos(2x)e2× dx

A:

Q: Se-3x cos(5x) dx

A:

Q: d) cos (5æ) cos(7r)dx e) S tan e sec“ rdr

A: we have to find the following integral