5. y ln x – x In y = In e2×

Q: d In (t2 + 1) dt = dx A) In(x6 + 1) B 3a In (a? + 1) 3x ln (a6 + 1) In (x® + 1) In (e? D -

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Q: 5). S 13+1)E dx (Improper Integral)

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Q: -Find the value of th integral e-x' dx.

A: Consider I = ∫0∞e-x2 dx                              (1) Let x2 = t On differentiating both sides,…

Q: 1.4 Calculate an approximate value of the integral S (sinx – Inx + e*) dx by - 0.2 dividing the…

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Q: 1 5 X If y = - find dy dx at x = 2.

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Q: 2- Find O for: y= In (x+5x) dx

A: Tpoic- Differentiation

Q: Find d if z = log2 y - 6 logs y. In In 64 dz dz dy y In 2 In 5 dy y In 2 In 5 O Option 3 O Option 2…

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Q: 1 (In x+1)x dy dx

A: Given integral is evaluated as follows

Q: 1) Find the following integals: 14) S(2? -x) dx le) S x* dx la) S x* dx Ic) )치 dr If) Sdx ax ti

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Q: d/dx integral from e to x^3 ln(t^2+1)?

A: If Fx=∫b(x)axf(t)dtthen dFxdx=ddx∫b(x)axf(t)dt=faxa'x-fbxb'x

Q: Find  dy dx implicitly. ln(xy) + 6x = 70

A: The given function is: ln(xy)+6x=70

Q: 3. Find the indefinite integral: Sx(x-2)* dx

A: Please rate

Q: dy Solve the differential equation = 9xy2 using the given boundary condition: y =7 when x = 3. dx…

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Q: b) Suppose x # 2. Find dif dx In y = In (x - 2)² √x² +1

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Q: dy y(ln y – In x +1) dx 1 C = -In None of the choices Option 1 1 C = -In C = -In- -ln Ontion3 Ontion…

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Q: 1. Evaluate S xe0.1% dx In x 2. Evaluate Sdx x3 3. Evaluate S x³(x² – 1)1°dx | 4. Evaluate (2 +…

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Q: 6 1) Find the general antiderivative for f(x) = 1+ x?

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Q: 1. Evaluate the integral |(x² - 5)e*dx 8.

A: Given that: ∫0∞ x2 -5e-3x dx To find: The value of the given integral. Let I = ∫0∞ (x2 -5)e-3x dx…

Q: 10. Find the derivative of y = ln 4**+1) In 4 dy A) dx 2x dy 2x In 4 B) dx dy 2xIn 4 C) dx 4(*+1) dy…

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Q: .2 -dædy In (x) ey

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Q: 2. * S arctan x dx 1 In(x²) + C C 1. x arctan x C A x arctan x -In(x² + 1) + C -- B 1 D x arctan x…

A: Solve the given integration

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y logy x * * -

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Q: 1) Find dy/dx if : y = ln (tan¬1 x)

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Q: 1. Evaluate 5 S Sx (x + 3x)dydx

A: Given, ∫05∫0x x(x + 3x) dy dx=  ∫05∫0x (x2 + 3x2) dy dx=  ∫05 ∫0x (x2 + 3x2) dydx= ∫05 ∫0x 4x2 dydx

Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

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Q: 1) Estimate In(1.1) using a linear approximation. 2) Let y = ln(x). Compute dy when x = e and dx =…

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Q: In 3 by Pots tien 3) S (4 - x)e"'dx calculate without integre (f Ju

A: Given,

Q: 19.) [(ycoth y² )log°(sinh y² )dy

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Q: In (6x) to x if y = sin (5e') dt.

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Q: Find So S 4:xy dx dy.

A: Evaluate the integral.

Q: dy y(ln y- In a+1) dx 1 C = -In 1 C = In O Option 2 Option 1 1 C =-In None of the choices O Option 4

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Q: 1) Find dy/dx if: y = ln (tan¬'x) 2) Solve the following integral dx xV25x² – 2

A: Find the integration using substitution method

Q: 6. Evaluate the integral e* dx ex + e-x

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Q: Eliminate the arbitrary constants x = -ln t , y = at + bt^2

A: given  x=-ln t , y=at+bt2 claim- to eliminate the arbitrary constants

Q: 6. Evaluate the integral. x³e2x dx

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Q: 16 Evaluate ſ," x²In 3x dx correct to three decimal places.

A: Given- ∫12x2ln3x To find- The value of the above integral. Concept Used- The above integral can be…

Q: 10. Find the indefinite integral 5x'e dx

A: Given,          ∫5x2ex3dx

Q: Sulve the dffeanlial equalion ly). clox Ylx)=16

A: Given:     dydx+y=16

Q: Find the indefinite integral x2e +e² dx.

A: The given indefinite integral is: I=∫x2e+ex dx

Q: (1 + 1 1 + In(x) + - X (x+y)ln(x) - 5y = c dx = (5-In(x)) dy

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Q: dy y(ln y - In x+1) | da

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Q: Find dy/dx for y = (ln x) 3

A: We have to find dy/dx of  y = (lnx)3

Q: dy Find in terms of x and y if x In y + yo = 4 ln x. dx

A: Solution is written in below steps.

Q: - if eV = In(x) + In(y) + e³ ху 3 Find dx

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Q: dy y(ln y – In a + 1) dx 1 C = -ln C = -In Option 4 O option 2 1 C =-In

A: This question is based on solution of differential equation.

Q: Can you help me step by step?

A: Let u=1+x^4

Q: 17. Integrate xylnx 3 X enfra W + C 3 2(1 x)² 3 2 ln x L +0 + C (In x)² + C

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Q: 4 16–x² Change the order of integration. Do Not Evaluate. 5tan xy dy dx

A: Answer