8. In each case use the given trigonometric substitution to evaluate the integral. You may assume that 0 < 0 < 5. (c) / ; (a) / ; - dx (put r = tan0] dx [put r = 5 cos 0] (a) (1+ x²) /25 – 22 ° (d) / tan 0] (b) JA- 12 dx [put x = 2 sin 6] dx [put x²/1+ x² r

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

A: see below the calculation and answer

Q: Find the indefinite integral. ∫(5 cos x − 2 sec2 x) dx

A: We first separate the integrals then integrate.  C=integrating constant

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

A:

Q: sin 3x (1+ 2 cos 3x)* dx

A: By using integration formula, we calculate the given integral.

Q: Find the indefinite integral. Solution in handwritten a. S sin x -dx cos²x

A:

Q: 3 Which of the following is equal to sec ² x tan³x dx to obtain the correct indef inite integral?

A:

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 integrals ∫sin4 2x cos 2x dx

A: I=∫ Sin4 2x Cos 2x dxLet Sin 2x=t2 Cos 2x dx=dtCos 2x dx=dt2

Q: S sin x In(cosx) dx

A: To evaluate the integral: I=∫sin x(ln (cos x)) dx Substitute  cos x=t⇒-sin x dx=dt⇒sin x dx=-dt

Q: 1 use this fact and the properties of definite integrals to evaluate 3 (7 - 6х2) dx. Given that x²…

A:

Q: Evaluate the definite integral (if it exists) 1/3 -4 sin(x) dz cos² (1) If the integral does not…

A: Substitute cos(x)=t⇒-sin(x)dx=dt At x = 0, t = 1 At x=π3, t=12 The definite integral is: I=4∫112dtt2

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…

A:

Q: Evaluate the indefinite integral sin (2)cos"(2)dz 4

A:

Q: Find integral of sin^2 (x/2) dx with bounds of 0 to pi

A: Find the integral of sin^2 (x/2) dx with the bounds 0 to π.

Q: Evaluate the integrals cos x dx 5. / sin x

A: since u have asked multiple questions in a single request so we will be answering only first…

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

A: The given integral is ∫cosxsin74xdx

Q: Evaluate the integrals ∫cos5 x sin5 x dx

A: Given integral:

Q: sin(1+In(2x))-/1+ln(2x)

A:

Q: What is the integral of sin^4(x)cos^3(x)

A:

Q: Evaluate the integrals ∫sin 2x cos 3x dx

A: We have to evaluate ∫sin2xcos3xdx. We know that 22sinA cosB=sinA+B+sinA-B Therefore,…

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: What is the integral of sin^5 x dx if the lower limit is O and the upper limit is T/2?

A: We have to find out

Q: 3 4. sin x cos xdx

A: These formulae are used while solving the question:

Q: Find the integral of 12 sin^5 x cos^5 x dx if the lower limit is O and the upper limit is T/2.

A:

Q: The definite integral sin24x cos2x dx is equivalent to x/2 (A -sin²0 cos²0 d0 2 x/2 В 2sin20 cos40…

A:

Q: 7. Find the integral of the hyperbolic function below. 6 sin(x) cosh[cos(x)] dx

A: Evaluate: ∫6 sinx coshcosx dx

Q: Find the indefinite integral. S-x² + sin x – 3* dx | In |x| – - 3* + C COS X - 3 In 3

A: detailed solution is given below

Q: 1) Evaluate the integrals: (a) f sin³ (2x) cos (2x) dx (b) sin³ (2x) cos (2x) dx

A:

Q: Find the indefinite integral. ∫cos3( x/3)   dx

A:

Q: Find the indefinite integral. x cos 10TX2 dx

A: We can find the integral as below.

Q: Evaluate the integrals ∫16 sin2 x cos2 x dx

A:

Q: Evaluate the definite integrals S(2sin(x)-3cos(x)dx

A:

Q: cos x dx

A: The given integral is ∫x2cos xdx We have to integrate the given integral using integration by parts

Q: 2) sin9xcos10xdx 3) sin xcos xdx XCOS dx 4) S

A:

Q: 4. Evaluate the integral: In6 -2x + sinh 2x|dx e2x + e-2x

A:

Q: Evaluate the integrals ∫(sin-1 x)2 dx

A: The given integral is To solve the given integral, use integration by parts method where

Q: Evaluate the integral. S sin (7x - 10) dx ㅇ cos (7x-10) +C -cos (7x - 10) + C cos (7x - 10) + C 7…

A:

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: Find the integral cos 10 using the substitution u = Enclose arguments of functions in parentheses.…

A: Explanation of the solution is given below...

Q: S sin x In(cos x) dx

A:

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

A:

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…

A:

Q: Suppose you calculated an integral using the trigonometric substitution x = 3sin(0), and got your…

A:

Q: Evaluate the integrals ∫sin3 x cos3 x dx

A:

Q: You found that the reduction formula of a certain integral is In = 180 (13x" sin (13x) + næ"-1 cos…

A:

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

A:

Q: 5 Only one of these calculations is correct to evaluate the definite integral x² In(x) dx 1 Using…

A: First we have to find h and it's corresponding formula.