Exercise 4: Integrate the following. dx (a) /= 16 х dr (b) / 5 + 2x4 et dx (c) / 1+ 2e2x cot x (d) CSc x + sin x dx sec2 x T9 - tan? a (e) dx dx (f) TV1- (In a)²

Q: 1 |dx I (sec² x csc* x.

A: Integration gives the function whose derivative is given. It is nothing but adding all to make…

Q: eXtan(e*) dx sec²(e*) – 7 2(, - 7

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Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: [ sin(lnx) x dx

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Q: 12. Given: f(x)dx = 4 S(»)dx = -1. and Find: (a)

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Q: Integrate sinln (10x) dx X

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Q: Find dy/dx of inverse tan(1/x) multiplied by secant(x)

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Q: Solve dx dy for y= sec (In x) In (tan x)

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Q: 2 sec2( sec-1x)dx xVx² -1 3. 3.

A: Here  we evaluate    ∫32 sec2sec-1xxx2-1  dx

Q: Integrate (sin1/2)(x)dx

A: The given integral is ,∫sin12x dx=∫sinx2  dx

Q: Solve d²y dx² cot x dy - sin² dx sin² x.y = cos x - cos³

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Q: (b) ( cosx) = -sinx dx

A: To Determine: find the derivative of cosx Given: we have a function cosx Explanation: we have a…

Q: (tan V) (sec V) b) Evaluate dx

A: Given integral: I=∫tan4(x)sec2(x)xdx

Q: use

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Q: x* + 4 dx : %3D 3

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Q: y=(sinx)x    d2y/dx2 ?

A: Apply exponent rule and solve:

Q: sec? (1/x) dx. 9: (16pts) Evaluate

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Q: 4 cos () dx 10. x³ sin3

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Q: S retan³ (e)sec² (e²)dx

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Q: -dx 1 – sin(0)

A: To evaluate the integral.

Q: +* dx f. 3x +. i. 3x sin x' dx

A: To evaluate the given integrals by substitution.

Q: / (cos(x) + Ex dx 4 +

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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: Find dy. y=tan-1(ex^10)   dy=(______) dx

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Q: - y = sin² (3*)

A: We have to find derivative of given function.