O dx √4-9x² O -1 sin O 1 sec sin 0 1 3 -sec 3x 2 2x 3 2x 3 + c + c +c 3x ¹ (³2) +c

Q: 2 х3 +3х6 1 x4

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

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A:

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A: The given integral is: I=∫x+1(x-1)(x2+x+1)dx

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A: Explanation of the answer is as follows

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A:

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A: ∫3x4+4x3+16x2+20x+9x+2x2+32dx

Q: i) S 3+6x+4x² −2x³ (x4+3x²) ·dx

A: The given integral is (3+6x+4x2-2x3)/(x4+3x2).

Q: 9x +1 d) / | 3 – g² + 9x – 9) x2 + 9x – 9) -

A:

Q: (a) Find 5x (7-2x)³ dx using the substitution u = 7-2x 3 → S(5x) (7-2x)=3dx

A: given integration

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A:

Q: 2x2 - x + 4 dx. x3 +4x Evaluate

A: ∫2x2-x+4x3+4x  dx

Q: 1 S dx = 3x+2 0-²(3x + 2) + C O 2√3x +2+c 3 O²(3x + 2)² + C A O√3x + 2 + c

A: The given integral is: I=∫13x+2dx  ...1   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: 4 sec 2x tan 2x dx (1+ sec 2x)²

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Q: x +1 8. J x(x+ 4)3 dx

A:

Q: Зx3—4х2+3х dx х2+1

A: Integration is a process of finding antiderivative of a function. There are basically two types…

Q: - 4x + 30 -dæ Evaluate (x – 5)(x + 5) + C

A: To solve the given integral first break the integrand into the simple expression using partial…

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Q: dx 1+x2 A In(1+x²) + c BIn(1+ x²) + c c tan-ix +c 1 x 2 D tan-x+ c IN

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Q: Evaluate D 6 |3x|√9x²-4 3 2 sin-¹3-sin-¹ 3 tan¯¹3-tan -1 1²/24 sec ¹3-sec dx sec-1³/12

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Q: 8x³ + 3x - 1 4x² + 1 dx

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Q: 2x2 + 3x – 3 dx X - 9

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Q: 1 x3 + 12x2 – 36x + 1 dx х2 + 4x — 12

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Q: dx (x-2)V4x²-16 is equal to 2 - -1 + C 4 sec

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Q: S (7z³ + 4x²) dx

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Q: S(cscr cot a +4x)dx sec a +x"+c 4. CSc a +x +c sec a+ x"+c O - sin a + a+c CSC a+x"+c

A:

Q: d. √ (1 + x)² dx √x

A: According to the given data, find the integral:

Q: cosxtanx - cos x= 0 + O 0+n,+ 2nx 5я O O+*5, + 2nx 5я

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Q: 1 Evaluate – -dx 1+ 3sin"x + 8cos™x

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Q: 2. 11+√7 dx

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Q: 2. Given that f is a differentiable function with f'(3) = -5, find g'(1) where g(x) = f(4x-x²)

A: The given function is,

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Q: Find dx O A. x-5- 15x2/3 1 5 -2/3 O B. 3 4x 3 5 -4/3 Oc. 3 3 5 -2/3 O D. - 16x-0 -* 5

A: