(5) Find the integrals: •ftan²(x) dx ● fsec²(x) dx • ftan³(x) dx ●

Q: dx sin*x

A: We have to integrate.

Q: y = Arctan(sec (3x)) +ncot(2x)

A: Given: y = tan-1sec3x + πcot2x To find: The value of dydx

Q: x*(1 + 2x') dx

A: This is the problem of definite integral with substitution. ∫01x21+2x35dx Substitute 1+2x3=t6x2dx=dt…

Q: Integrate S x sin(x)dx

A:

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

A: Integral by parts

Q: 101 Jzy cosu(x) + sinh(x)

A: Given differential equation:d2ydx2-y=coshx+sinhxTo find: General solution. Note:1 coshx=ex+e-x22…

Q: 1. (2x + 1)(x - 5) dx

A:

Q: find dy/dx y = ecos(x+sqrt(x+lnx))^3

A:

Q: (3x + 1)'3 dx

A:

Q: find the general solution of  xdy/dx+4y=(sinx/x)*(sqrt of y)

A:

Q: Integrate cot(r) In(sin(x))dx.

A:

Q: fx- sin(2x ) dx

A: Given that  The integral is xsin(2x^2) To evaluate the integral

Q: (x²-ax +4" dx

A:

Q: / x(8x + 9)" dx %3D

A: Using Liate's rule for integration we can solve the above problem. This is also known as the…

Q: Show that cosh (3x) = 4cosh³r - 3 cosh T.

A:

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

A: We separate the differentiation with both parts

Q: SVx In(x)dx

A:

Q: 1. ſx3 tan-1x² dx (Integration by Parts)

A:

Q: Y = √²n²√x+1

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: у %3DIn(In sec x)

A: