In x /1+ (In x)² -dp-

Q: (In x)* Integrate: 1

A: Given,            ∫1eln x4xdx

Q: 2. Evaluate the integral 4 dx V2x-5 5/2

A:

Q: Evaluate the integral of ax^2 e^-bx dx

A: We will use the "integration by parts" method to find the evaluation of the integral.

Q: (22-4) (교3-4z)3 dz

A:

Q: To evaluate the integral 1. 7 64 + x² -dx,

A:

Q: Find the indefinite integral: 10sin 3x - 15 cos 2x + 6 e5x + C O 90sin 3x -60 cos 2x + 150 e5x + C…

A: 30∫cos3x+sin2x+e5xdx=30· ∫cos3xdx+∫sin2xdx+∫ e5xdx=30·…

Q: -25 Evaluate the integral: dax x²Vx2 +25

A:

Q: Compute 3 In(x² + 1)dx=

A:

Q: 5. Show that dS = 0. lav

A: The objective is to show that, ∮∂VdS=0. Let V=cT where c is a constant vector. Now by divergence…

Q: 3. Integral xdx 10x -234

A: We will use substitute method to solve this integral.

Q: Compute integral23  3x^2+2x+1 / x^2 dx

A:

Q: 1. Evaluate the integral 5x + 1 dx 2x2 - x -1

A: We can evaluate the given integral by using the partial fraction method.

Q: Evaluate the indefinite integral S(z -9-dz 를-9z + 듣 +C 4x4 중-9z + + C 222 - 9x + 7lnx³ + C - 7 9x -…

A: First we write each term using exponent

Q: Consider the indefinite integral *7x³ + 9x² + 12x + 24 -dx x4 + 4x2

A: Given,            ∫7x3+9x2+12x+24x4+4x2To find : The partial fractions decomposition.

Q: Evaluate the integral. 了學 ( Inx dx O- In x - +C 2x 4x2 O-4 In x - + C 4x2 0.을 Inx- +C 2x2

A:

Q: Find the indefinite integral: O 10sin 3x - 20 cos 2x +6 e5x + C 90sin 3x 60 cos 2x + 150 e5x + C…

A: The objective is to find the indefinite integral.

Q: evaulate the indefinite integral  4x^3+2x^2+6x-5/(x^4-x^3)

A: Firstly, We factorize the denominator

Q: 3 2 Evaluate the improper integral: dx Ji33x– 1

A:

Q: Compute integral-11  3x -√1-x^2  dx

A:

Q: Compute integral23   3x^2+2x+1/x^2  dx

A: The given integral is ∫233x2+2x+1x2dx.

Q: Find * In(x² + 2x + 2) dx (x + 1)² In|1 + (x + 1)²| x +1 In|1 + (x + 1)2| x + 1 + 2tan-(x + 1) +c…

A: I am attaching image so that you understand each and every step.

Q: у" - In x

A: Given: y''=lnx

Q: Evaluate the integral: Sen(1²2+3x-7) е dx A x² + 5x+In 3x-6|+C XZ B +5x+31n|x-2|+C 2 C x ²2+ = +…

A: On solving this we will get

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: the Fundamental Theorem of Ca -5 (x³ – 9x)dx. v3

A: Here we have to use fundamental theorem of calculus to find the exact value of  ∫05(x3-9x)dx…

Q: dx 3-2x-x2 -3

A:

Q: 9 In(z² – 1) dz

A: Given: ∫9lnx2-1dx

Q: Use (3) from Section 5.4 to evaluate the integral: -7/9 dx %3D 4.

A: Given integration is : ∫47x-79dx To find the value of integration.

Q: Evaluate the integral dx 2x리x-3월 x2 1 3 + V2x In A + C 2/3"3 - V2 | ® In(2x x - 3{x²) +c 1 In + C…

A:

Q: Show that L₁J - dx x² + 2x + 2 = In(√5-2).

A:

Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

Q: Evaluate the integral. 3x-7 (a) S- dx x2-2x-8

A: Answer and explanation is given below..

Q: 2. Use Theorem 4 to evaluate (3x +2x2) dx

A: Given ∫01 (3x+2x2)We know that ∫xn=xn+1n+1+C

Q: 16. Integral Ydy 6y2-1

A:

Q: Evaluate the integral. dx 7 6 36x - 49

A: Given

Q: 1. Express into parital fraction. Hence evaluate y2 -4 *2-4

A: according to our guidelines we can answer only three subparts, or question and rest can be…

Q: Evaluate the integral. '3 4,3 3,2 dt -

A:

Q: Show that dx = x² – 8x In (7 + 4/3). -

A:

Q: 6. Evaluate the integral dx (4x2 + 1)(x² + 4)

A:

Q: 7. Evaluate the integral. Vx2 – 25 dx х3

A: First we will make a trigonometric substitution of x=5*sec θ then we will solve it and integrate it.…

Q: 19. f(x. y) In(1 - x - y) %3D

A: As per our company guidelines we are supposed to answer only the first question that you have…

Q: Evaluate the integral: Sen(+²+2x-7) ox dx A x² + 5x + In|3x-6|+C B +5x+31n|x-2|+C X + +In|3x-6|+C Ⓒ…

A:

Q: Find the interval and radius of conv. of In(1 – x²)

A: The power series representation of given function ln1-x2 is given by: ln1-x2=∑n=1∞-x2nn

Q: 5. prove that d (-x) (+ x) = X dx dx d² dx² - x² +1

A:

Q: 19. Consider the integral f√x²+25 dx. 9x² a. In/√x² + 25 +x/- - b. x+ In/√x² + 25/+ √x²+25 9x √x²+25…

A: Solve the integral  √(x2+25)/9x2

Q: Find the integral. [(3 - 7x° + 5) dx 7 OA. 9x° -**5 7x* +5x +C O B. °-** 7 + 5x +C OB. Oc. 9x°. -**…

A: According to the properties of integration we have: ∫[f(x)±g(x)] dx=∫f(x) dx ± ∫g(x) dx

Q: 2x²-3x + 10 dx (x²+4)2

A: The objective of the question is evaluate the indefinite integral.

Q: Prove that: 3-4x² dx 4VIn3

A: The given integral is I=∫0∞3-4x2dx. The idea is to evaluate the above integral using gamma function.…

Q: Evaluate 1-(In x) x In x -dx

A: