Solve the LDE = dy/dx = [1/(1+x³)] – [3x?/(1 + x²)ly %3D

Q: Find the indefinite integral sec* 7x dx.

A: To find the indefinite integral of ∫sec47xdx

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

A: Integral by parts

Q: > Evaluate the Antegral dx ax45x +2

A: Rewrite the given integrand as follows. 32x2+5x+2=32x+1x+2=22x+1-1x+2

Q: 70ot(*) e*dx e2x +1

A:

Q: Find dy/dx by implicit differentiation. 4x2 + 3xy - y? = 2 dy/dx =

A: We have to find derivative

Q: find the length of the curve y = arcsin e^(-x) from x = 0 to x = ln 5/4

A: Given curve, f(x)=arcsin e-x from x=0 to x=ln54

Q: Integrate O sinh 2x dx

A:

Q: arccos 2x dx 3.

A: We will use integration by parts. The solution is given below.

Q: Evaluate the integral.

A:

Q: sinh In(2+2x) dx? x+1

A:

Q: S sec x dx Use Integration by parts to solve

A:

Q: Evalualte! dx cosX x+ メ+ 1

A: Given:

Q: Calculate dy/dx Simplify y=3x-5/2x+4 dy/dx=

A: Solving by derivative we have

Q: Solve th D.E using Exact dx +(x² +3y* )dy

A:

Q: 2 dx =

A:

Q: b) By using appropriate substitution, solve the integral 7x dx. (1–4x)"

A:

Q: Find the indefinite integral. sinh(4 - 7x) dx

A: evaluate the indefinite integral ∫sinh4-7xdx

Q: The integ ral csc(0.5) dx is equal to

A: Follow the procedure given below.

Q: xe dx

A: In the given question we have to solve the integral s.t ∫xexdx. we will solve the indefinite…

Q: Ssin x CosX dx 6x dx

A:

Q: arctanx e dx (1+x²,"

A: The given problem is to evaluate the given integral. We have to evaluate by using substitution…

Q: Find ∫cosh 2x sinh2 2x dx.

A: To find the value of the integral∫cosh2xsinh22xdx

Q: (log a) dx 1+x²

A:

Q: The Smith's invest $10,000 in an account that grows to $12,000 in 5 years. What is the annual…

A: Consider the given smith invest $10,000 in an account that grows to $12000 in 5 years

Q: Find the indefinite integral.

A: Use the substitution method and consider x2 as u. Differentiate both sides of u=x2 and substitute x2…

Q: 4 dx X-X-2Ą

A:

Q: Find the indefinite integral. sinh(4- 5x) dx

A: To find:∫sinh4-5xdx

Q: •2 5. Calculate | x In(3x)dx.

A: Given integral:

Q: Use an appropriate substitution to integrate 12 x*(x++ 1)°dx

A: The given integral is 12x3(x4+1)9.

Q: 2. Jx sinh x2 dx

A: ∫x sinh x2 dx

Q: (a) Find thne derivative. y = In(4x – 6) – 3 In(x) dy dx

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

Q: Find the indefinite integral. ∫sec x/2 dx

A: Given ∫sec x/2 dx. We need to evaluate the above integral.

Q: Find the value of the definite integral: 4x dx -2

A: ∫-254x3 dx

Q: 1. S =dx = -Arcsin x√x²-4x-1 +2 X √5 +c

A:

Q: show that d/dx arctan (tanhx) = sech (2x)

A: On differentiation, we get

Q: q² In(x³ + 1) dx

A:

Q: Evaluate the integral. sinh 5a -dx +C. 5x

A: Evaluate the integral the given function Sinh is hyperbole function.

Q: Solve drc dt dy dt 200 +

A:

Q: - Find dy/dx for y = log2(1 – sin³ (3x²) %3D

A: Use the chain rule to differentiate the given function.

Q: Integrate: cos Gx) – sinh(2x)]g

A: As per our guidelines only one question can be answered.Please repost the next part in next…

Q: for dx

A: Given integration is : ∫exdx To find the value given integration by parts.

Q: Find dy/dx implicitly. 9xy + ln(x2y) = 7

A: The objective is to find dy/dx implicitly.

Q: SOLVE USING INTEGRATING FACTOR 2. (2y2 + 2 In x +1) dx +2xydy = 0

A:

Q: Compute dy/dx for y = log3 x

A: Our Aim is to calculate dydx for the function given below:-y=log3(x) -(i)

Q: Find dy/dx Y=tan^-1 ( ln 7x^5)

A: If y = tan-1 (x) then dy/dx = 1/(1+x2)

Q: dy/dx for (ln(tan(2x)-sqrt(3+e^2x) / (pi(x)^3-cos^2(-5x))

A: Given,     y  =  ln(tan2x)-3+e2xπx3-cos2(-5x)

Q: Find dy/dx by implicit differentiation. 11 11 dy/dx = (Express your answer using positive exponents…

A: The given function is 11x3+11y3=7

Q: Without integrating, explain why

A: when the integration is in the form  ∫-aaf(-x)=∫-aa-f(x) is odd then it is equal to 0

Q: Solve the definite integral e(arcsin(x)) dx. /1 – x²

A:

Q: Ssin(3x) sin(7x) dx

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.