EX, find dy for y=x. Cos'ex - √1-4x² di

Q: dy Q10., Solve (1+ x²) + y = tan¬1x. dx

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Q: s.fx 5. x3 sin 3x dx

A: We have to find the indefinite integral

Q: find dy. y = 3 csc (1 - 2√x)

A: We use the chain rule

Q: So 0 xe- dư x²

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Q: find dy dx Y = √x tanx+ === ye х 2

A: given  y=x  ×tanx+1xformula used→(i) d dx(xn)=nxn-1(ii)  d dx(tanx)=sec2x(iii)  d…

Q: Sx sech2 x² dx

A: Given:  Integral of xsech2x2

Q: find dy. y =2√x/3(1 + √x)

A: we have to find the derivative y=2x3(1+x)

Q: 4. Find / 4 5x² dx. (36x² +20x) 7 ár.

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Q: .2 dx Jo (9 + x²)2

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Q: /9-x² dx. Use trigonometric substitution. x2

A: This question is related to indefinite integration, we will we will solve it using given…

Q: 3. tan x dx

A: Formula: tan2x=sec2x-1

Q: -dx x +1 2 5.

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Q: Evaluate Set 7x cos (6x) dx. Sex cos (6x) dx =

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Q: EX: using the relation I= Vn show that J1(x) = 2 sin x

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Q: sec2 ) 15. Evaluate. - x2 dx

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Q: y = cos(-4x)

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Q: Q.2: Evaluate: -2 2 dx 1 I = x2 - 8.

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Q: dx It sin x-cos x COS

A: To evaluate:∫dx1+sinx-cosx Solution: We know,cos2x=1-tan2x1+tan2x     ...(1)sin2x=2tanx1+tan2x…