Use a change of variables to evaluate the following integral cos x) sin x dx 5 -(cos 'x-5 cos x-c (cos 7x-5 cos x- cos x) sinx dx 5 (Use C as the arbitrary constant.)

Q: 5) find the integral J8 sin 2x * cos2x dx

A: see below the calculation and answer

Q: Find the indefinite integral. ∫cos3 x sin4 x dx

A:

Q: Evaluate the definite integral. π/2 1- cos(2x) dx

A: Answer:-(1) Given the integral,     ∫sin2x cos22x dx=∫44*sin2x cos22x dx…

Q: Evaluate the integral. |cos 7x cos 3x dx

A: The given integral ∫cos7xcos3xdx.

Q: Find the integral of x^2 * cos(4x) dx.

A: To compute the indefinite integral.

Q: Use integration by parts to show that for n > 2: / sin" x dx: 1 sin- x cos x + /sin-2 x dx.

A: To evaluate: ∫sinnx dx

Q: Find the indefinite integral. ​ integral of sin^3(4x)*cos^4(4x)dx

A: Important points for the question: 1. sin2 x + cos2 x = 1   sin2 4x + cos2 4x = 1 2. ∫xn.dx =…

Q: .2 x cos 9TTX dx

A:

Q: Evaluate the definite integral: cosx (1 – 2 sinx)² dx

A: To solve definite integral we take sinx=z then we substitute all the values of x by z ,then we…

Q: S cos(2x + 3)cos(3x – 5)dx

A:

Q: Use integration by parts to evaluate the integral: sin(In(9x))dx 1 x(sin (In)(9æ))– cos(In (9x)) + C…

A:

Q: 4. sin 4x cos 3x sin 2x tan 3z dx

A: Given, I=∫sin4xcos3xsin2xtan3zdx I=tan3z∫sin4xcos3xsin2xdx now solve this integration we know,…

Q: Evaluate the integral: CT/2 cos² (4x) sin³ (4x) dx.

A:

Q: 1 x² cos(x³) dx CoS

A:

Q: Find the indefinite integral of (1+sinx/cos2x) dx

A: We have  I=∫1+sin xcos2x dxI=∫ dx+∫sin xcos2x dx   Substitute  cos x=t sin x dx=-dt

Q: Evaluate the integrals ∫cos3 x sin x dx

A:

Q: What substitutions are made to evaluate integrals of sin mx sin nx, sin mx cos nx, and cos mx cos…

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Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x"-1 sin x…

A:

Q: [ cos² 2x sin² 2x dx

A:

Q: Evaluate the integrals.∫cos x/sin7/4 x dx

A: The given integral is ∫cosxsin74xdx

Q: Find the indefinite integral. X cos 8TX2 dx

A: To evaluate the integral: I=∫x cos 8πx2 dx⇒I=∫cos 8πx2 x dx...(1)

Q: dx 2 sin x+3 cos x-5

A: Here we going to use some arrangements, look at the all steps carefully

Q: Evaluate the integral. integral  cos 3x  sin 2x dx

A:

Q: Evaluate the integral. integral 0  to pie /2     sin 3x  cos 2x dx

A: Consider,

Q: Find the indefinite integral

A: To find the indefinite integral: ∫sinx7+cos2x dx Solution: Let substitute t=cosx Differentiating…

Q: Find the indefinite integral. ∫cos5 x sin x dx

A: ∫cos5x sinx dx Put, cosx=t⇒-sinx=dtdx⇒-sinx dx=dt⇒sinx dx=-dt

Q: Find the indefinite integral ∫cos 2x cos 6x dx

A: Given integration as I=∫cos 2x cos 6x dx Since  2cos 2x cos 6x=cos 6x+2x+cos 6x-2x…

Q: 1+cos 4x dx 1-cos 4x 10.

A: Evaluate integral

Q: Find the indefinite integral. | x cos 9x² dx

A: Given : ∫xcos(9πx2)dx

Q: 3 2 1. + cos x) dx x3

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Evaluate the integral sin x dx (2 + 3 cos x)2

A:

Q: Find the indefinite integral.∫ 8x cos2x dx

A: To integrate the indefinite integral: ∫8xcos2xdx

Q: Evaluate the integrals. ∫x sin x2 cos8 x2 dx

A: Given,         ∫xsinx2cos8x2dx

Q: Evaluate the integrals.∫x2 cos x3 dx

A: We have  I=∫x2cosx3 dx                          ⋯⋯(1)   Let  x3=t3x2du=dtx2du=dt3 put in equation…

Q: Evaluate the integral/ cos'x sin x dx using the substitution u = cos x. cos"x sin x dx =

A: ∫cos11xsinxdx

Q: cos (6x) cos (3x)dx

A: Solution :∫cos6xcos3xdxNote…

Q: Evaluate the integrals ∫cos x cos 7x dx

A: To integrate: ∫cosxcos7xdx.  We know that cosacosb=12sina+b-sina-b. Therefore, using the above…

Q: Find the indefinite integral ∫ cos2 x sin4 x dx

A: Given: I=∫cos2xsin4xdx we know that ∫sinnxdx=n-1n∫sinn-2xdx-cosxsinn-1xn                   ..1

Q: TC 4. sin(2x) cos(2x) dx

A: To evaluate the definite integral

Q: Evaluate the integral of sin(4x) cos(3x) dx

A: We have to use 2sinAcosB= sin(A+B)+sin(A-B) formula to simplify first.

Q: Evaluate the integrals ∫cos3 2x sin5 2x dx

A: Evaluate: ∫cos32xsin52xdx

Q: 14. Use a suitable change of variables to determine the indefinite integral. fsin²xcos³ xdx (Hint:…

A:

Q: Integrate by parts f(x)=sin4(x)cos3 (x) dx

A: Given the integral  I = ∫cos3(x) sin4(x) dx cos2(x)=1−sin2(x) I = =∫cos(x)(−sin4(x)(sin2(x)−1)) dx…

Q: Match the integral expression on the left to an equal expression on the right. cos(7x))dx + cos(…

A:

Q: Match the integral expression on the left to an equal expression on the right. cos(7x))dx + cos…

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Q: Evaluate the integrals ∫sin3 x cos3 x dx

A:

Q: cos 4x cos 6r dx

A: NOTE: Refresh your page if you can't see any equations. . use the formula

Q: sin(3x)sin(4x)dx Ssin(3x)cos(4x)dx Jcos(3x)cos(4x)dx

A:

Q: 2 sin6 x cos⁹ x dx 0

A: See the details solution in below

Q: Find the indefinite integral. J. x cos 107Tx2 dx

A: