Find the indefinite integral by making the substitution x = 9 sin e. 6. V81-x2 1 3/2 +C 81 V81- 81-x2 + C 81x 1 3/2 + C 81- 81x +C V81 - 81x + C

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: 2. Find the following indefinite integrals. 1 dx (a) 16 – [In(x)]² 1 xp (b) | x?+ 2x + 26 / A 1 (c)…

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Q: 14e" dx 1+ e20

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Q: 5 Find the following indefinite integrals. 10 a. f(x+2)' dx b. J d. [4 (3-&x) dx c. (3x-7) xp-

A: c)

Q: 1. Find the following indefinite integrals (any 4) +3x ii) [(2{/x* - 7x' +10e* – 1)dx iii) [(x²…

A: To evaluate the given indefinite integral.

Q: Find the following indefinite integral. (5 -0.25x Jox=D -0.25x +3e d%xD (Type an exact answer in…

A:

Q: 1. Find the definite integrals of the following functions : (a) L. 4.x dx (h) dx ex +1 -2 0. (b) /…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: 3. Find the indefinite integrals. (a) /4 dx (b) /2* r 2x-x2 dx

A: Given two functions integrate it by use of formulae

Q: Evaluate the definite integral. cln 8 So° f (x) dx, ƒ (xæ) =6e* /(5+e*)

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Q: Find the indefinite integral. 3 8 dt = t3 t2 +C

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Q: 1 Determine the definite integral of 4 3(Vx) xp (DE + x^)S

A: Let I=∫49x+13xdxApply the Sum Rule:…

Q: 16 – x2 dx - Evaluate the integral: 9x?

A: (A)  x=4sin(θ) (B)  19cot2(θ) (C)  -19θ-19cot(θ) (D)  -19arcsin14x-16-x29x

Q: Find the indefinite integral. | 15 7 19 – 14 d t8 - dt

A: We have to solve the integral

Q: Evaluate the integral. x2 cos(6 x) dx + C

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Q: Calculate the definite integrals (a) I₁ =¹7 (2x − 1)(x + 2) dx - 18 (b) I₂ =2₂¹8 (x + 2)(√√x - 2) dx

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Q: Consider the following. 0.4 x2 xp V4 - 25x2 4 – Let x 2 sin(0) and determine the following. dx = de…

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Q: Find the following indefinite integrals if a, b and c are positive real numbers, with a +-1 and b +…

A: Note that a≠-1 and b≠ 1    then we can solve these integral

Q: 1. Use formal substitution to find the indefinite integral (a). de f(-6a) (r-3) de (b)

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Q: 10) Evaluate the integrals by substitution 2 -dxp 3 -2 (x² + 2)° a)

A: We have to evaluate the integrals by substitution method: ∫-22xx2+23dx Assuming, t=x2+3 Then…

Q: Find the indefinite integral.

A: Given : ∫e2x1+e2xdx

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

A: Given ∫e-θ  Cos 2θ dθ

Q: 2. Find the indefinite integral (Scos(4x) + √x dx

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Q: In evaluating x- 2 dx by substitution, if u=x- 2 then what will be the resulting indefinite integral…

A: We can find the answer as below.

Q: 7 For the integral 3xVx + 6dx, if we use the substitution u = x + 6, we can rewrite the integral in…

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

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Q: find the indefinite integrals. 1. ∫ e−0.05t dt 2. ∫ (3/t  -  2/t^2)  dt

A: case 1:The given indefinite  integral  is ∫e-0.05t dt.Let u = - 0.05t, then du/dt = -0.05.

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: d) Determine the infinite integrals of the following e+2 i. ii. 2 3 sin2x dx

A: Evaluation of the integral

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

A:

Q: 7. Evaluate the definite integrals: a) L, (x2 +1) dx b) 3x dx

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Q: 5. Evaluate the following indefinite integrals. 8. **** Power 2 ...... sin.x dx. b-₁f.co₂x² dx…

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Q: Find the indefinite integral. a. -+c -7x + C e а. 1 b. -7x + C 7x 1 -7x - +C с. 7 d. -7e-1x + C e.…

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Q: Evaluate the integral analytically. 1 е бх 1+ e 6x

A: consider I= ∫01e6x1=e6xdx

Q: Evaluate the integral of (e^x)^(1/2)

A: Given the integrand (e^x)^(1/2) Evaluate the given integral using u-substitution method. Let

Q: 11. Evaluate the definite integral J, 02 1 -dx. 1 x+a²

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Q: (а) 4x³ dx -2 (b) | (2г° — Зг + 6) de (c) | (2г — Зг + 6) de

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Q: Determine the following indefinite integral up to a constant c: / sin (2x). Select one: O…

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Q: 4 Consider the indefinite integral x° · Vx* + 2 dx: This can be transformed into a basic integral by…

A: We will solve the problem.

Q: 1. Find the following indefinite integrals (any 4) (2/x* - 7x' +10e* – 1)dx (x* + 1)e* iii) dt +3x…

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Q: 1. Evaluate the following definite integrals. 214-2*|x dxr

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Q: 1 (x² +a) b dx is In 5x The resulting integral of +eTan-1 + C, where a, b, d, and e are integers. x³…

A: Given:∫5xx3+x2+4x+4dx= ln⁡x2+a1bx+d+eTan−1⁡x2+C Let, I=∫5xx3+x2+4x+4dx ⇒I=∫5xx2(x+1)+4(x+1)dx…

Q: 2. Use the substitution method to determine the following indefinite integrals: (a) / cos(2r) dæ (b)…

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

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Q: 1 4 dx 2 /1 – x²

A:

Q: Find the integral of (1 + 2x)e^(-x) dx from x-0 to x--. A. 3 B. 4 C. 2 D. 1 O A B. DI

A: Use integration by parts for solving it,

Q: e) S 7 + 2sec(2x)tan(2x))dx 1+x

A: To find: ∫71+x2+2sec2xtan2xdx

Q: 2. Find the following indefinite integrals. (a) / sin(In(x)) xp (b) / º etan-(x) dx x2 + 1 sin(t)…

A: (a) ∫sinlnxxdx Let; lnx=t⇒1xdx=dt     =∫sint dt=cost+C put again: t=lnx =coslnx+C Result:…