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

Q: Find the indefinite integral by using the appropriate formula

A: Given: ∫cos4xdx   Formula used: cos2x=2cos2x-1   cos2x=1+cos2x2

Q: Compute the indefinite integral, and demonstrate that your solution works by differentiating:…

A: Since you have asked multiple question As per our policy , we will solve the first question for you.…

Q: Use a Table of Integrals to evaluate the integral. sin(3x)dx

A: To evaluate: ∫e6xsin3xdx Let, I=∫e6xsin3xdx Integration by parts states that…

Q: Evaluate the indefinite integral. sin(-3x) dx +C.

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Q: Use the Table of Integrals to evaluate the integral.  ∫ Sin-1 √x dx

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Q: sin 0 -do 4+cos 0 Evaluate

A: Since 4+cosθ is never zero in 0 to 2π as -1≤cosθ≤1. So, 3≤4+cosθ≤5 So, sinθ4+cosθ is analytic in 0…

Q: sin(3x) dx 1+cos²(3x)

A: We have to evaluate the given integral using inverse trigonometric functions-  ∫sin(3x)1+cos2(3x)dx…

Q: dx V1-e2x

A: A detailed solution is given below.

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: Solve the integral 6. sin10 x cos° x dx

A: To solve∫0π2sin10x cos9x dx

Q: sin-3/2x cos³x dx

A: Given integral

Q: What is the integral 5 tan^4x dx?  Integrate and find the indefinite integral.

A:

Q: Solve the integral by using integration techniques

A: We have to solve

Q: Evaluate the integral -4 sin(5x) sin(2x) dx

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Q: evaluate the indefinite integral.

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Q: sec2(Arctan x) dx 1+ x²

A: We have to use integration by substitution technique. we can use substitution for Arctan x.

Q: Find the integral ∫dx/sin22x without using a substitution.

A:

Q: evaluate the definite integral from [0,pi] [(sinx)2(cosx)4]

A: To integrate the definite integral

Q: Evaluate the indefinite integral: ∫(θ + sec2 θ) dθ

A: Our Aim is to evaluate the indefinite integral given below:-∫θ+sec2 θ dθ  -(i)

Q: Find the indefinite integral ∫tan3 2t sec3 2t dt

A: We have to evaluate ∫tan32t sec32tdt Given integral can be written as: I=∫tan22tsec22t sec2ttan2t…

Q: Find the indefinite integral ∫ sin x /(7 + cos2x) dx

A: To Evaluate: Integral ∫sin x7+cos2xdx                                                   (1)

Q: sine da Seco co?o

A:

Q: Evaluate the indefinite integral. ∫sin5(x)cos4(x)dx

A: Integrate the given indefinite integral as follows.Consider the expression sin5(x)cos4(x).The above…

Q: cOs x In(sin x) dx

A: Given,  ∫cos x ln(sin x) dx

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

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

Q: Use the Table of Integrals to evaluate the integral.  ∫ sin6  2x dx

A: Consider the provided integration, ∫sin62xdx Find the value of the provided integral. Apply the…

Q: Ssin( /3x)cos(-2r)dx

A:

Q: Find the indefinite integral by using the appropriate formula . ∫ x2 sin x dx

A: Solution -    Given Indefinite Integral- y=∫x2sinx dx Integrating using by parts formula which is…

Q: Use integration by parts to solve the indefinite integral of [sin5xcos3x]dx

A:

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. Sinx cossx xp-

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Q: Evaluate the indefinite integral. sin°(13x) cos“(13x)dx

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Q: Find the indefinite integral. sin3 70 V cos 7e de

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

A: The given integral is,

Q: Evaluate the indefinite integral tan" (2x) dx

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

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Q: Calculate the integral ∫dx / sin4x+cos4x.

A: Given,   .

Q: Determine the following indefinite integral.

A:

Q: Evaluate the integrals ∫sin3 x cos4 x dx

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

A:

Q: Evaluate the indefinite integral.

A: It is required to evaluate the indefinite integral:

Q: Solve the integral: dx

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 trigonometric integral ∫sin2 x cos3 x dx

A: We have to find the trigonometric integral: ∫sin2 x cos3 x dx Rewriting the integral, ∫sin2 x cos3 x…

Q: Evaluate the integral:∫sin3x dx.

A: The given integral is ∫sin3x dx

Q: Evaluate the definite intégral. 2 cos -(x) -dx 1 - 1 V1 – x2

A: In the given question, concept of Definite Integral is applied. Definite Integral A definite…

Q: Evaluate the integrals ∫sin3 x cos3 x dx

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Q: Solve: the integrand (pi/3 sin5x) dx on the integral pi/2 to 3pi/2

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

A: