(4)Evaluate the definite integral (a)(1+ si 0 1+ sin x)dx (b) (2t+cost) di (b) f( -x/2 x+ X - dx R/4 sec²0 (d) f -do tan² 0+1

Q: Find tan-1 x2 -dx using integration by parts.

A: Integral by parts

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A: Given gx=lnx3+sinx-3tanx3x4-x We know that lnab=lna-lnb. Therefore, using this formula we can write…

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A:

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A: We have to find

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A: Please see the explanation below.

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A:

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A:

Q: integrate (cos (x)/(sin(X)-cos(x))

A: Integration is a technique of finding a function  the derivative of which, , is equal to a given…

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A:

Q: 3. Sx² tan (3x-1) dx

A:

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

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A:

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A: the question is taken from the derivative in which we have to find the derivative of the given…

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A: 1. ∫sec2x dx=tanx 2. ∫sinx dx=-cosx 3.∫(u±v)dx=∫u dx±∫v dx 4. ∫abf(x) dx=F(b)-F(a), where ∫f(x)…

Q: 1) Find the derivative of f(x) = 1+sin 2x %3D 2 cos3 x

A:

Q: 2, " cos“(x)sin*(x)dx

A: To find : ∫0π2cos6xsin4xdx

Q: Show that d/dx(x arcsin x+√1−x2) =arcsin x.

A: We separate the differentiation with both parts

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A: we have to integrate

Q: Find f. f"(x)  =6 x + Sin x

A: Given: f"x=6x+sinx we know that f'x=∫f"xdx                                      ..1 so, by using…

Q: Determine the derivative dA/dx if cos²x sin(x²) 7x3 tan x A = sin 3x In x² 2x² +8 e¹-2x] 52x+1]

A:

Q: (b) 1:16 tan5(x) sec²(x) dx

A: 1621​ or if you have needed in decimal form then you type 0.00617283 round as much you need.…

Q: 2 X (x-sinx)2 | 6x'sin² 2 3/2 - Evaluate: +3x dx. X, X-sinx

A: