d dx -1 (sin-¹ (²)) = A B C D 2(1) 1+(-4) ¹ 2(1) √₁-(4) 2 (4) cos¹ (1) 16 -2 (1) cot (1) csc (16) 16

Q: Evaluate / 4 x cos(x)dx Ox sin(x) – 4 cos(x) + c 04 sin(x) + 4 x cos(x) + c 04 (x sin(x) + cos(x)) +…

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Q: 2x + x2 cos(x) + 1 -dx x2

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Q: te √e³x Evaluate 3x cos 4x dx.

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Q: (sin())= d.r

A: We apply chain rule here .

Q: Ssin(2x+3)dx= d -1 cos(2.x+ 3)+C 2 a 5 cos(2.x + 3)+C -1 cos(2x+3)+C - cos(2x+3)+ C e cos(2x +3)+ C

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Q: dx 4. -' (x- 3)*

A: Solution is given below

Q: In * (X+2)7 (x+2)7

A: Note Hello experts!!! As per our guidelines we are supposed to answer?️ only one question. Kindly…

Q: 2. 1 Evaluate the definite integrals below. Use u-substitution when appropriate. 4 5 3el/x (a) (b) |…

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Q: Let h(x) f(æ) If f(x) = 3 cos (x) and g(x) = 3x + 2x2 – x + 4, what is h' (x)? (æ)6

A: Given: f(x)=3cos(x)g(x)=3x3+2x2-x+4   Let h(x)=f(x)g(x).   Then, h(x)=f(x)g(x)=3cos(x)3x3+2x2-x+4

Q: (3) csc (3x) dx = A) In csc (3x) + cot (3x)| + C C)-In |csc (3x) - cot (3x)| + C B) - In |csc (3x) +…

A: We will solve this question by substituting the value of 3x.

Q: dx x4+16 Įtan-( x2 + c 4

A: Given that, ∫xx4+16dx

Q: 3. Find the derivatives: a) f(x) = 3x³-4 2x²+3 b) DO NOT SIMPLIFY y = (x² + 6x + 2)(²+√x + 3) c)…

A: Given; a) f(x)=(3x3-4)/(2x2+3) b) y= (x2+6x+2)(2/x4 + 3sqrt(x5) +3) c) g(x)=-2csc7x+8sin3x+12tan2x…

Q: Q# (13 Rewrite: cos (x)sin(x)dx A) ſ u'du 1/2 B) Tu°du V312 C) [ -u°du 1 V3/2 D) [ u°du 1 V3/2 E)…

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Q: 2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan…

A: We can find the answer as below.

Q: Q1) Evaluate: (a) fe²_1_dx Inx sin ¹x 1-x² dx (b) f 1- cos dx (e) Jỗ 2sinx cosx dx (c) | Inx dx

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Q: (cos(20))(sin(0) + cos(8))ª de

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Q: b) if J(zf64)} - 39ga) ) ce = Sin () %3D and S(3f (x)+9 6)) dx = tan () 2. 2. +596)) dx

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Q: 1 sin(x) (D²+1)³

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Q: d (c) (cos(2²) + In(3 – 2æ)) dx

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Q: 2x sin-1(x²)dx =

A: This question is taken from the indefinite integral in which we have to choose the correct option…

Q: Find the value of f(0) when 3 sin(2t), f( f'(t) 1. f(0) 2. f (0) 3. f (0) 4. f(0) 5. f(0) = = = = =…

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Q: 1. ſ X (2x-5)² (3-4x) dx.

A: Solution: ∫x(2x-5)2(3-4x)dx Take the partial fraction ∫398(2x-5)-514(2x-5)2-349(4x-3)dx

Q: (sin 31)8(1-a/2)dt

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Q: dx Evaluate V- x² – 4x – 1

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Q: (D4 + 18D2 + 81)y = 0 (A y = (c, + c,) cos3x + (c,+c,) sin3x. (B у %3 (с, + сх) cos:3x + (с,+c)…

A: To solve the given differential equation first we construct auxiliary equation and then solving the…

Q: f (t) =-e" sin (21 +7)

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Q: 1. (D² - 4D+5) (e² sin x)

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Q: COs ax dx. x² + b² (q)

A: Cauchy residue theorem: If f is holomorphic function defined on simply connected open set with…

Q: (b) Verify that f(x) = 2 cos(x) sin(1x). f(x) = sin(6x) + sin(7x) = 2 sin = 2 sin 6x + N 2 X COS 6x…

A: Given

Q: Evaluate (i) dx S √e xlnx√(2lnx)² – 1

A: We are asked to evaluate the integral

Q: Differentiate the functions. a) f(x) = 2 – 5x + b) f(x) = e* + cosx c) f(x) = d) f(x) = (5 – x²)· e*

A: Suppose f and g are differentiable function .Then note the following results : The power rule of…

Q: Find a general solution of the given ODE: (a) y"-3y" +4y'-12y=30 cosx-16e²* (b) y"+2y"-y'-2y=14e*…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: OY O (-9)" (2n)! (a)ea (b) cos 3 (d) sin 3 (e) None (c) cos a

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Q: 1- (sin (Cos(2x)+Cos (sinc2x)

A: Given derivative

Q: (d) ƒ COS √1+sin x dx, (e) cos(lnx) S dx Т

A: