1 5. S z dx x²(5+x)3

Q: 10. Evaluate the integral. dx x²/4 – x²

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Q: 7.S dt J VE+2- 5

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

A: Tpoic- Differentiation

Q: 7. Evaluate the Integral S (x + 3) dx

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Q: find integral x3 3) S dx /1-x²

A: We have to find the indefinite integral

Q: 3. Evaluate the integral Sx cosx dx.

A: Please see the below picture for detailed solution.

Q: Evaluate the integral : S 8г2 +10х—6 (х—1) (х+1)2 dx = |

A: The given integral is ∫8x2+10x-6x-1x+12dx.

Q: 14. Evaluate the integral: (x² + 3x)° dx A. (x* + 30)' + C 3 x* + 3x' + C C. +C (x² + 3x) + C В. D.

A:

Q: 5) Find the general antiderivatives for the following; х-1 dx x* +2х-3 -dx 6)

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Q: 5. (5 – x)² * 6 Show that if y=3-x then %3D 6. . (x-s) _ xp 1. dx. 3 Hence, find the value of , 2(5…

A: In differentiation use quotient rule In integration use substitution

Q: 2 Evaluate the integral S (3x³ – 2x² + x) dx. 1

A: We solve it by integrating polynomial

Q: Find g'(3). g(x) = In(1+t) dt In(4) 6ln(10) O In(10) 3

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Q: 14. Find X(s), given x" + 16x = t, x(0) = 0, x'(0) = 0.

A: answer is in next step

Q: 1.5 3-y Q1) Evaluate the integral dx dy

A: To evaluate the given integral.

Q: 15. sin(2t + 글) dt = e2t-3 8. 7 4 7 64e3 7 4

A:

Q: 36 – y8 -dy y5 Integrate:

A: SOLUTION-

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: 1. Determine the following: 8. S(V)° -+ - 9 7 dx (4x-1)3. 2-x 2x5-4Vx+3 h. S

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Q: 2(1-z) Evaluate S S --) dy dx dz

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 12. Find the integral of S (x². √(x² + ² =) dx

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Q: | Va(In(x))° dr (ax) 1.

A: We find the integration by substitution.

Q: In x /1+ (In x)² 6 S -dx

A: Given query is to eveluate the integral.

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: 1 Find xIn(x15) dr. xln(x!5) 1 а. xIn(x!5) 1 -In] In(x!5) |+ C 15 1 dx = In] x'5 |+ C b. xln(x!5) 1…

A: Use the substitution method and integrate the given expression.

Q: s at x =-1 and x = 2

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Q: (-1)" S. =È D n=1 Vn +1

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Q: 3.53 dx Compute 3+9,2

A: I=∫013313+9x2dx=19∫01331x2+13dx=19∫01331x2+132dx Since, ∫1x2+a2dx=tan-1xa

Q: 16 9. Evaluate the integral 4 dx.

A:

Q: 4 a2 Calculate the integral: dx (2² + 7)/2 4 Va2 + 7 a) Vz? + 7 +C + 4 ln V7 4 x b) O x + Vx² + 7 +…

A: From the given problem:   I=∫4x2x2+732dx ........(1)   Let,…

Q: 18 2 6x dx using n = 2, 4, and 8 subintervals 2

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Q: In x Compute -dx. 3√√/x 9 X 3 A²x²0 nx-x²²+ C A.- In 2/3 2 4 1 B.- - +C X 3 4/3 4 3 C.--(In x)x-4/3…

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Q: 2 16n |xV8 - x³ dx: 9/3 3 11) Show that

A: Properties of Beta Function:  β(m, n)=∫01xm-11-xn-1dxβ(m, n)=Γ(m)Γ(n)Γ(m+n) ;       m>0,  n>0…

Q: ( 5 sin 3 (t - ), 0, t 4 6. If f(t) = 4

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Q: 1?+Az-5 dx 23-1 Evaluate: 글 미교2 2 + 11| + 5v3Arctan (똥(2z + 1)) +C 글피교2 + z+ 1|- 3v34rctan ((2z +…

A: The area under the curve fx between two fixed limits is called the definite integral. A definite…

Q: 3. Find the integral x² +12x +12 dx x' - 4x

A: Given,            ∫x2+12x+12x3-4xdx

Q: 2. Evaluate the integral x(3 – 5x) (3x – 1)(x – 1)2 dx

A: To solve the following integral

Q: 6. Evaluate the integral. x³e2x dx

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Q: −x^2+x+6 has root(s) at x=

A: To find the roots of the given equation.

Q: 4. So -dy Vy+1

A: To evaluate: ∫01yy3+1dy Substitute y3=u2⇒13y-23dy=2u du⇒13u4dy=2udu⇒dy=6u5du. As y→0⇒u→0, y→1⇒u→1…

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

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Q: 3. Calculate S x²sin(x³ + 1)dx.

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: dr 21. (1+x²)/16 – (tan-l r)² dx e2x+2+2 22. 8. dx x2 - 6x + 25 23. 6. 24. dr J (2 - r)V - 4x +3 dr…

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Q: 8. Evaluate the integrals. * Sx³ (x² + 1)5 dx

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Q: -X +7 Evaluate the integral: dx (x-2)(x+3) In x - 2|+2 1n x +3 +C 2 In |x – 2| – 2 In |x + 3|+C 2…

A: First of all we will do partial fraction, then we will evaluate the integral.

Q: 6. x sec x tan x dx

A: Let's find.

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

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Q: .4. (c) y = x*; y = sin(Tx/2); about x = -1

A: