Integrate the function. -B3/2 dt

Q: Find the derivative of the function. u4 + 8Vu f(u) = 8.u10 +14. 4" – 24. 1u -9. uT - 4 e" + u2 F(u)

A: givenf(u)=8u10+14(4)u-24(π)u-9uπ-4eπ+u4+8uu2diffrentiate with respect to u we know d(xn)dx=nxn-1and…

Q: 7/2 sec*(t/2) dt

A: Here we will solve the given definite integral,

Q: Find the derivative of the function. f(u) = (6u + 9)3/2 + (u2 − 6)−3/2

A:

Q: 2° dt

A:

Q: Find the derivative of the function. u4 + 9Vu f(u) = 9-u11 +17. 64 – 27. 1u -11. u – 6 eT + u2 F(u)…

A:

Q: Integrate the function. 2 – 25 dx

A:

Q: Find the derivative. d 3 (1²+71) -5 dt -5 13 (1²+71) = dt

A:

Q: Make a substitution first. Then use Integration Tables. dr = +C x® + 9

A: 1/3 (ln x^3 + √(x^6 + 9)) + c

Q: Find the first and second derivative of the function. G(r) = Vr + Vr 1 + 1 G'(r) = 3x G"(r) =

A:

Q: dx Integrate V2 18x2

A: we have to integrate

Q: d Calculate dt

A: To calculate  ddtt2et

Q: 6. S t √1+2t dt

A: The given integral,    ∫t1+2t4dt

Q: Evaluate fcos-¹(x) dx

A:

Q: e-st cosht dt

A: Integration basically means to find the integrals, i,e. to assign numbers to function in such a way…

Q: Perform the integration. 2 - x dx x2 – 4x

A:

Q: Integrate the function. dx ,x> 6 x2/x2 - 36

A: Given: ∫1x2x2-36dx , x>6

Q: Use logarithmic differentiation to find y'. y = (x² + 2)°(x² – 8)7 %3D -

A:

Q: Find the derivative of the function. t3 h(t) = t8+5, 5,10+ 152 h'(t) = %3D (+5)2

A: Given: ht=t3t8+52

Q: Integrate the function. 88 dx

A: Solution: The objective is to find the value of the given integral

Q: Differentiate the function. (2x+5) y= (5x+1) 3 기 dx 11

A: Given:       y=2x+545x+13 differentiating with respect to x Apply the quotient rule:…

Q: Evaluate the function: 1 dx x²/3 () 1+a!/3

A: Given: ∫1x231+x13dx

Q: Calculate the derivative. d (17t5 – 19t3) dt dx

A:

Q: Find the first and second derivative of the function. G(r) = Vr + Vr G'(r) G"(r) II II

A: For this problem, we will use the following result: ddxxn=nxn-1     for all real n.

Q: Why does dA/dt = 0?

A: Since area is constant therefore dA/dt=0

Q: Integrate the function. 2 + 16 dx 2x2

A:

Q: Next, simplify. - 3t dt = dx

A:

Q: Integrate the function. 9-x dx, x< 3 x4 27x3 OA. (9 -x²) 3/2 (9 - x²) 3/2 O B. x3 + C (9-x²) 3/2 +C…

A: Recall: ∫ax+bndx=an+1ax+bn+1

Q: 5. csc 4x dx

A:

Q: dx Vx²+9

A:

Q: ) dt 5e + 1+ t2

A: Take the help from standard form of integration and simplify.

Q: dx1 -2x1 – 2x2 X(0) = dt dx2 2x1 – 6x2 %3D - dt

A:

Q: Sea-teln(t)dt

A:

Q: 2x 5. F(x) = "(5t – 1) dt

A: Here, it is given that F(x)=∫x2x5t-1dt

Q: Find dt

A: We have to slove derivative

Q: Find the first and second derivative of the function. G(r) = Vr + V G (r) =

A:

Q: Find the first and second derivatives of the functions in Exercises q² + 3 p = (q – 1) + (q + 1) -

A:

Q: dP dt

A: Given differential equation is: dP/dt = kP - m ................ (1) where k and m are positive…

Q: V27x° dx

A: Using power function formula of integration.

Q: 6. dx Vx - 1

A: Given that I=∫161x2-1dxsolution…

Q: dx1 -4x1 + 2x2 X(0) = | 2| dt dx2 + 2x2 dt II II

A:

Q: LA PLACE TRANSFORM

A: we have to find the inverse Laplace transformation of the given function.

Q: Find F'(x). F(x) dt

A:

Q: Calculate the derivative. h(t) = 5et−3

A:

Q: sec+estnx dx secx

A:

Q: x2 dx Vx2+12

A:

Q: dx x2e

A: The given integral is: ∫1x2 e1xdx To integrate this, assume 1x=t On differentiating both sides.…

Q: - Integrate the following function: -3 2x+3 dx y = Jo x²+3x-5

A: The given integral is: y=∫032x+3x2+3x-5dx To evaluate this integral, consider x2+3x-5=t   .....(1)…

Q: + 3x² dx -2+ Ix) dx (scc² t -1) dt

A:

Q: Evaluate: fxea dx. Show all steps, and explain yourself.

A: Given: The integral ∫xe3xdx, To evaluate: The given indefinite integration.

Q: dx 1. dt 4.x1 – 2x1.x2 dx2 -2x2 + 8x1.x2 dt

A: This is a problem of system of differential equation.