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[arcsin(2x + 1)]

A:

Q: y=(sinx)arctanx

A:

Q: |5sin(4x + 5) sin(2x --) dx

A: We need to evaluate the given integral. We will use the formula  Cos(A+B)-Cos(A-B)=-2 SinA SinB

Q: x3=sin2 y differentiate?

A:

Q: By using tabular method, evaluate -3* sin(27r)d.r.

A: The integration by parts is done using the formula: ∫udv=uv-∫vdu.

Q: cos(2x) dx sinx+cosx

A: Given: ∫cos(2x)sinx+cosxdx

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: 3 cos° tdt 5. 1+sint

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: csch (2 sin2x) dx 1. V1-4x² r(²-1)cos[cosh (In r)]dr OS 4.

A:

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

A:

Q: sin(7x 2) dx cos2 (7x 2)

A: Let u=cos(7x+2)differentiate both sides w.r.t. x.Use chain rule for cos(7x+2)From there we get du/-7…

Q: Evaluate and Graph ¹) S ( sin x (1-x) dx dy do

A: Given: ∫01∫0ysinx11-xdxdy. To Evaluate: The above integral. To Sketch: the graph of the region of…

Q: (sin A)^4-(cos A)^4

A:

Q: m) -dx 1+sin(2x)

A:

Q: (Sin ² x - y) dx - tanx dy =o

A:

Q: -S * sin ´sin sin (e*) dx

A: we have to integrate

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

A: To evaluate the given integrals by substitution.

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

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: (b) / sin (50) do

A:

Q: sec x tanx (1+sec'x)² + sec

A: substitute u= sec3(x)+1 du/dx=3sec3(x)tan(x) dx = du/(3sec3(x)tan(x)) put this in equation  1/3∫…

Q: e cos (2x) dx

A: The given integral ∫e-xcos2xdx can be evaluated as, Let,  I=∫e-xcos2xdx By applying integration by…

Q: Evaluate:

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