4. Determine the following indefinite integrals: a) S(2x* + 3x³3 – 7x² + x – 5) dx b) S(x – 5)² dx • (In x)² c) S*-**2 dx x²-7x+2 h) Sx²e*x° dx d) S 4x(2x² + 3)³ dx i) Sx*(x° + 10)5 dx e) S dx 6x2 dx 3+2r3

Q: Compute.  integral (ex) / (1+e2x) dx.

A: Solving an indefinite integral using a substitution. If we have some function defined as:…

Q: how I calculate the definate integral 3x^2-e^2x(dx) on the interval ln3 to 0

A: To find the definite integral

Q: 3 Estimate the integral 1 dx by the trapezoidal rule using n = 4. + 1 Vx3

A: ∫abf(x)dx≈Δx(f(x0)+f(x1)2+f(x1)+f(x2)2+f(x2)+f(x3)2+⋯+ f(xn−1)+f(xn)2) where ∆x =b -an

Q: 1. Evalute the improper integral 3x dx. 1+ x2 -1

A:

Q: (5) Find the indefinite integral (a)f Vtan x sec²dx (b)fem2* sec² 2xdx sin x (c) Cos x 1 cos-do 0 2

A:

Q: Use any method to evaluate the integrals ∫ 2x - 2-x/2x + 2-x dx

A:

Q: 18) Use two compositions of composite Simpson's method to estimate the integral Inx dx

A: The Simpson's rule can be used to calculate the integral approximation. The formula used in…

Q: What are the new limits of integration after applying the substitution u = 5x + z to the integral s…

A:

Q: What is the integral of x2(2-x)^(1/3) dx on the interval [1,2]?

A:

Q: Can we evaluate the integral of 1/(x^2+2x)^3/2 dx by using x= sec¿ - 1

A: Consider the equation

Q: 3/ Find Valke of integral Sx dx

A: Value of the integration

Q: 5. Write down an integral that can be solved by usingintegration by parts with u = x and another…

A: dv=x dx

Q: 1. Evalute the improper integral 3x dx. 1+ x2

A: Given: ∫-1∞3x1+x2dxTo evaluate the improper integral:

Q: 34. x sec xdx

A:

Q: Queston} $²3 20c x²-4 Composite Trapezoidal rule with n=4 dx. 3.1.1. use the to approximate…

A:

Q: Use trapezoidal with 3 level romberg (k=3) to evaluate the integral from lower limit 0 to upper…

A:

Q: Evaluate the integral: f sin 7x cos 2x dx. A) sin 5x + sin 9x + c. 2 B) cos 5x +co cos 9x + c. 10 C)…

A:

Q: 1) Evaluate each integral by substitution: (In x) dx a)f(x+1)(x +2x)'dx b)fxVx² +9dx 「ズ dx 7x+5 dx…

A:

Q: 33. Use integration by parts to find the indefinite integral. fxcos(2x)dx -xcos(2x)–sin(2x)+c а. b.…

A: To find the integration

Q: Evaluate the integral. Sex. cos 3x dx e2x [ sin 3x + cos 3x] + C O e2x [3 sin 3x + 2 cos 3x] + C 13…

A: Given: ∫e2xcos3x dxe

Q: 3 Estimate the integral 1 dx by Simpson's rule using n= 8. Vx3 + 5

A: Given that a integration and ask estimate value use Simpson rule when n= 8. In Simpson rule we can…

Q: Evaluate the integrals ∫(sec2 x) etan x dx

A: Evaluate: ∫sec2xetanxdx

Q: Find the indefinite integral using integration by parts with the given choices of u and dv. |x…

A:

Q: Find indefinite integral.

A: ∫5lnz+3z dz Put, 5lnz+3=t⇒5·1z+0=dtdz⇒1zdz=dt5

Q: Evaluate the integral. 3x cos 2x dx O e3x [2 sin 2x - 3 cos 2x] + C 13 O 1 [2 e3x sin 2x + 3 cos 2x]…

A:

Q: s/4 dx 2- 1+tanx 3.

A:

Q: Evaluate the integrals: 1. 2. -2 dx 0 8+2x² x+3 2x3-8x S - dx

A:

Q: Evaluate the integrals that converge: 3 dx 2x ! b) | a) dx (x² + 5)³ 3 – x -00

A:

Q: х — 3 х3 -4х

A:

Q: 2. Calculate the indefinite integrals for the following functions as integrands: 1 x In ¤/(In x)2–1…

A:

Q: 7. Find the indefinite integral. (a) + sec , | dx = 4 In |x| + tan(x) +C (b) / )Lanr dx = In |In x|…

A: Given that: (a)∫4x+sec2xdx(b)∫1xlnxdx(c)∫x4-3x2+5x4dx

Q: 4. Evaluate the improper integral. dx х2 — 1

A: Consider the given integral as Solving the integral

Q: Match the integral expression on the left to an equal expression on the right. Ssin(3x)sin(4x)dx -…

A: Let's find.

Q: 4. Determine the following integrals 4.2 - dx - a x

A:

Q: The integral of the given function csc °x dx is equal to 3cos x-10stn²x cos>x-15sin"xcosx + C…

A: I=∫ csc6x dx =∫ (cot2x+1)2 csc2x dxu=cot xdu=-csc2x dx=∫ -(u2+1)2 du      =∫(-u4-2u2-1) du…

Q: 9. Use Simpson's Rule to approximate the integral f Vx3 – 1 dx withn = 6.

A: We have to find the value of given integral using Simpson's rule.

Q: csch (2sin 2x)dx 1. V1-4x

A: Given problem:-

Q: 8. [In(x² + 1) dx

A: Formula for Integration by parts: ∫fg'=fg-∫f'g

Q: Use any method to evaluate the integrals ∫ x4 - 1/x5 - 5x + 1 dx

A:

Q: 5. Find the particular integral of d²y + dy - x2 + 2x + 4 dx2 dx

A: We use the operator method to find the particular integral of the given differential equation.

Q: Compute the definite integral 2 dx Vx² + 4

A: First, we need to compute ∫xx2+4dx

Q: 1 dx x+1 1

A: Evaluate improper integral

Q: 9. Write as a single integral in the form f(x) dx. 2 5 -1 f(x) dx + f(x) dx f(x) dx -3 f(x) dx

A: The given expression is ∫-32fxdx+∫25fxdx-∫-3-1fxdx. Write the expression in a single integral. The…

Q: 4) Reverse the order of integration in 2 2x x' dydx 0 x2 and evaluate the integral as an x-simple…

A: To reverse the order of the below integration. ∫02∫x22xx3dydx

Q: Evaluate the following Integrals: 1. (sin(4t) – 3 sin(2t)“ dt 6. Vsech(4x) tan (4x) dx 3 sin sinh 3y…

A:

Q: Evaluate the improper integral s dx -2 (2+1)4/3

A: Given: To evaluate ∫-201(x+1)43dx

Q: ∫−∞0 (2x/(x2+5)3) dx

A: Given,   ∫−∞0 (2x/(x2+5)3) dx

Q: Compute integral x^2cos(x^3+3) dx

A: Given : ∫x2cosx3 + 3dx

Q: (6) Find the indefinite integral - 3x+2 x+1 12x-22x dx (O) 3x -11x +15 x' +2x +3 dx (c)+3x +9x x In…

A: Solution is given as below: