In evaluating / *sin³(2x)cos(2x) dr by substitution, if u = sin(2x) then what will be the resulting indefinite integral in terms of u and dư? %3D (A u³ du u³ du © :/ u3 du

Q: Evaluate the indefinite integral. 3x sin(4x)dx

A: The given integral,      ∫e3xsin(4x)dx

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

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

Q: Solve: The indefinite integral of the integrand (cos x/1+sin2 x) dx

A:

Q: Find the indefinite integral.

A: To find the indefinite integral: ∫5cosx - 2sec2xdx Solution: Evaluating the integral. ∫5cosx -…

Q: Find the indefinite integral.

A: According to power rule of integration .

Q: Find the indefinite integral and check the result by differentiation. 3 3 dx (5 – 9x2

A: Given               ∫x(5-9x2)3 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: evaluate the indefinite integral.

A:

Q: Find the indefinite integral using the formulas from Theorem 5.25. (Use C for the constant of…

A: Given:      ∫51+e2xdx

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: evaluate the integral: integral of 8x*sin^2(x)dx

A:

Q: the integral of sin5(2x)cos4(2x)dx

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: 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: Evaluate the indefinite integral given below. Provid [(-3x - 3)¹ dx

A: Given indefinite integral is ∫-3x-34dx We can solve using substitution method ∫xndx=xn+1n+1+C

Q: Find the indefinite integral by making a change of variables.                             ∫ cos3 2x…

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Q: cos xdx sin x

A:

Q: Evaluate the integrals ∫cos5 x sin5 x dx

A: Given integral:

Q: Use a table of integrals with forms involving eu to find the indefinite integral ∫e−4x sin 3x dx

A: By using the table of integrals we are to find the indefinite integral: ∫e-4xsin3x dx

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: Evaluate the indefinite integral: ∫(sec2 θ) etan θ dθ

A: we have to find the indefinite integral ∫(sec2 θ) etan θ dθ

Q: Evaluate the indefinite integral given below. 12 sin (2x) dx V1– 4x2 -

A: Given Data The integral is ꭍ-12sin-1(2x) dx /√(1-4x²).   Let,

Q: Find the indefinite integral using the formulas from Theorem 5.25. (Use C for the constant of…

A: We need to evaluate integral.

Q: Find the indefinite integral by the method shown in Example 5. XVx + 3 dx

A: Given,          ∫xx+3dx

Q: Evaluate the indefinite integral by using the given substitution to reduce the integral to standard…

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Q: Find the indefinite integral ∫cos4 x dx

A: Given- ∫cos4x dx To find- The value of the integral. Formula Used- Using the reduction formula, we…

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: What is the definite integral of sin^5 (x) cos^3 (x) dx if the lower limit is zero & the upper limit…

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Q: Find the indefinite integral S (8x2/3 + 5* – cos(x))dx and verify the result by differentiation.

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Q: Compute the indefinite integral. ∫(1−sin2x)/(cosx) * dx

A: The given integral is,

Q: Find the indefinite integral and check the result by differentiation.                     ∫(1 +…

A: ∫1+6x46 dx Put, 1+6x=t⇒0+61=dtdx⇒6=dtdx⇒6 dx=dt Therefore, ∫1+6x46 dx=∫t4 dt=t55+C=1+6x55+C

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

A: We can find the integral as below.

Q: 6. S COSX dx sin2x

A: Solving the problem by finding the value of the integral.   NOTE :: As per our Expert guidelines we…

Q: Evaluate the integrals ∫sin3 x cos4 x dx

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Q: Evaluate the indefinite integral sin2 x cos x cos xdx =

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Q: Find the indefinite integral using any method ∫cos x ln(sin x) dx

A: Given, ∫cos(x)ln(sin(x))dx

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

A:

Q: In evaluating/ *sin³(2x)cos(2x) dr by substitution, if M = sin(2x) then what will be the resulting…

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Q: Find the indefinite integral. X COS 9TX

A: Given,I=∫ xcos9πx2dxPut…

Q: cos(9x) -dx COS J 1+ sin²(9x)

A:

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

A: Evaluate: ∫cos32xsin52xdx

Q: Find the indefinite integral by the substitution method or state that it cannot be found by our…

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Q: Find the indefinite integral using any method ∫√(1 + √x) dx

A: Given: ∫ 1+x dxBy using the Substitution methods:Put   1+x =t…

Q: Find the indefinite integral. 8x In (5x)dx

A: The given indefinite integral is ∫8xln5xdx.

Q: Evaluate the indefinite integral: [ 10 10e¹x cos(2x) dx

A: We will use simple Integration rules to solve this question.

Q: Evaluate the definite integral. In 3 6e-X cosh x dx

A: Given integral is- I=∫0ln36e-xcoshxdx where coshx=ex+e-x2 Thus,…

Q: Evaluate the integrals ∫sin3 x cos3 x dx

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Q: tan 0 . Find the indefinite integral by using the substitution x = xp: (1+ x2)?

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Q: Evaluate the indefinite integral sin5 s cos sds %3D

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Q: Use one of the formulas in the table above to integrate dx x8 + 16 (By the way, you're going to need…

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