Evaluate the following integral. |5 cos (5x)dx 5 cos (5) dx |(Use C as the arbitrary constant)

Q: Evaluate the given integrals. 1. cos 2x dx

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: e) TT/2 cos x In(sin x) dx t/4

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Q: Evaluate the following integrals: a) cos (5x) dx b) 3x sin(2.x) dx - Sa x-7 c) dx (x+4)(x- 3)

A: Integrate in the following way:-

Q: |(x² + 2x) cos(2x) dx

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Q: dx 1 = S- g2+x2

A: Solve

Q: Q1: Evaluate the following integrals by substitution dx 1. e cos e*dx dx 3. J 2x- 3

A: Solve by substitutions

Q: Evaluate the following integrals using techniques studied x(x+ 5)* dx 2. 4x cos (x² + 1)dx

A: Given: 1. ∫xx+54dx2. ∫4xcosx2+1dx

Q: Calculate the following definite integral: |x² – 1| dx -2

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Q: Evaluate the integral [e2 cos(2x)dx.

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Q: Evaluate the following integrals: S cos“ : x dx 1-

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Compute the indefinite integral of the following function. r(t) = (4 sin t,3 cos 8t,7 sin 6t)

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Q: Evaluate the following Integrals 1 I. dx 1-cos x

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Evaluate the following integrals: (a) dx x²/x² – 16 - (b) sin x cos xdx (c) x – 3 x² + 6x + 5 -

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Q: 2 X COS x dx ах

A: To integrate: ∫0π2x cos (x) dx

Q: [sin(In x)+cos(In x)]¯ dx

A:

Q: |-e+2 COS X 3 x- Sin x

A: Let,

Q: 4. S)(1-x²)dx 5. S(e2t)dt

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Q: Evaluate each of the following indefinite integrals. (a) / 12 x²(3x³ – 5)% d (b) / 2t sin(t²)…

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Q: A. Evaluate the following integrals: 1. sin 'xcos x dx

A: Given: I=∫sin7xcosxdx   ....(1)   We know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: 1. Compute the following integrals. (a) sin (e) dx. 4 dx. - (b) x2

A: we have to calculate integration

Q: Evaluate the integral. x2 cos(7 x) dx +C

A: The given integral is: I=∫x2 cos(7x) dx

Q: Evaluate the integral. ∫e-θ  Cos 2θ dθ

A: Given ∫e-θ  Cos 2θ dθ

Q: 1. Evaluate the following integrals. ? cos(r) dt а. Зx2 — 1 dx b.

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Q: evaluate the given integral.

A: To evaluate the given integral

Q: Evaluate the given integral. ∫ (e2x cos x -2e2x sin x)dx.

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Q: EVALUATE THE INTEGRAL

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Q: Evaluate the integral. x² cos(3 x) dx =| + C

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Q: Find the following indefinite integrals. dx = (m) / (~- (bị + 3e" + dt =

A: (a) I1 =∫x3-1xdx (b) I2=∫eπ+3e2t+1etdt We know that  ∫xndx=xn+1n+1+c and ∫enxdx=enxn+c

Q: Determine the following particular integrals: -{3x²e-x} 2.1 2.2 1 D² + D-1 1 D² - D+2 {8 sin x cos…

A: To Determine: the following particular integrals:   2.1 1D2+D-13 x2 e-x 2.2  1D2-D+28 sinx cosx

Q: Evaluate the given integrals 1 -dx b. Į S7-2 cos x

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Q: 3. Evaluate the following integral using the Beta function: /2 sin 20 cos 40d0

A: According to the trigonometric identities sin2x=121-cos2x, cos2x=121+cos2x and…

Q: tan 2x dx 2. S (3+ln cos 2x)6

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Q: Evaluate the following integral using the Fu 9x/2 | (cos x- 4) dx -9x/2 9x/2 | (cos x- 4) dx = -9x/2…

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Q: Evaluate the definite integral integral a=0 and b=1    7/ 1+x2 dx

A: Refer to the question, we have to solve the definite  integral a=0 and b=1    7/ 1+x2 dx.

Q: Evaluate the following indefinite integral: dx r2 +1

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Q: Evaluate the following definite and indefinite integrals. (a) / sin(x) cos(x)ešin(=) dx (b) L. V5/2…

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Q: 6. Evaluate the following integrals: (a) /sir sin³ x dx

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Q: 1 dx x² +1 e +

A: solution:-∫02ex+1x2+1dx=∫02exdx+∫021x2+1dx=ex02+tan-1x02=e2-e0+tan-12-tan-10=e2-1+tan-12     Ans

Q: Evaluate the following indefinite integral. -x-2 (a) dx dx (b) cos 0 sin Od0

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Q: Find the indefinite integral. ∫e4x cos 2x dx

A: Here given integration as I=∫e2xcos 2x dx

Q: | -2" dxr. (x² + 1)e

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Q: Compute the definite integral below using the results in S '5 I x² dx

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Q: 3) Evaluate the following integrals. a) | cos(tan(x)) sec (x) dx

A: Given that ∫cos(tanx) sec2x dx first let us simplify and then integrate

Q: Evaluate the following definite integrals. (а) |2t – 4| dt. /- (b) cos(3x) dx. (c) d.x.

A: You must have an idea about definite integral to solve these questions. In these types of integral…

Q: Evaluate the following integrals. Tt/42 cos x dx e* 2 cos а. S dx V1-9x²

A: We have ∫0π42 Cosx dx Now, ∫0π42 Cosx dx becomes  ⇒2Sinxπ40                         as ∫Cosx…

Q: 1. Evaluate the following integrals: g) . dx sin-1 x V1 – x2

A: Since you have posted more than one question we solve the first one for you. For the remaining…