Vx(4- x)dx 2x e - 1 ,2x +1 e

Q: dx 2. 16e* +e-*

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Q: 1 dx - X+ 4x - 3

A: Given: ∫1-x2+4x-3dx

Q: dx 3. If 8c²xy = (x² - y2)2, find- dy

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: a-) I = c6 Vx²-9 dx 3 b-) S x In(x² + 1) dx

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: dy 3. + y = e3x dx

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Q: dx dw x'V4-8x (25 + w* } 2.5 V16-9x2 dp- dx 2х (6x -x²)"* 3/2 2. dx 3.5 (5– 4x²)"a 3/2

A: integration

Q: H-w 2x +3 dx メ+2 X X 3 X2+ 2X+1

A: Topic:- application of integration

Q: d -[x*] = xx"-1 dx

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Q: 3x +2 J. - dx. (x² +9)(x– 4)x 10. Find the principal value of

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Q: Vx - 3 dx x=3

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Q: 1) f3x* dx +x dx 3) fxva² +I dx

A: We know that, ∫ xn dx = [( xn+1 )/( n+1 )] + C

Q: 4x x*e*dx (2sin dx V4-x2

A: We can solve all the intregration problems with tha mathod of substitution. In substitution we use a…

Q: 3. dx (x²+1)² -3 d x XVX +3, dx x2

A: Evaluate the given integrals

Q: dx i let x-= 4X-X2

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Q: d, 3 Find dx -)- + x(х - 1)). A -3 +2х-1 B +1 -3 +1 -6 +2х-1 x3 (D

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Q: Vx - 2 dx 5 x*(Vĩ + 1)

A: I have stated the used formulas in the solution

Q: 3 V1+x³ [6] S dx > x-2

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Q: S(-5)'r dx 6x-9 2. Í dx x-3x+5 1.

A: ACCORDING TO THE GUIDELINES WE ARE INSTRUCTED TO ANSWER ONLY ONE QUESTION OR 2 SUB- QUESTION, THE…

Q: (iv) S х2 +3х-1 dx x3-1

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Q: d²y - x² = 0 with dx2 (x = -3) = 2, y(2)=4 dx

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Q: αdx = x x2-a2 dy

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Q: dx 1- S 4+x2

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Q: 3/2 (-2x + 4) dx J1/2 | 16.

A: Note: We are authorized to answer one question at a time, since you have not mentioned which…

Q: x dx 5. J 3-x2-6x

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Q: -1)/(x4))1/2

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Q: x+2 a) f- =dx V2x-x² |xIn(x+1)dx b)

A: Given that  (a) ∫(x+2)/√(2x-x2) dx   (b) ∫x ln(x+1)dx Here we have to calculate the given integral.

Q: 3 - dx x² – x - 2 (1) (ii) fx'e* dx

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Q: d -(f(x² + 3x)) dx

A: Derivative

Q: x(3-5х) J - (3x-1)(х-1)* # 2) Evaluate: -dx-

A:

Q: (3x4-43)dxc+(xy²-2x?4)dy:

A: 3xy2-y3dx+xy2-2x2ydy=0 fx,y=Mdx+Ndy ∂M∂y=∂N∂x For M=3xy2-y3∂M∂y=6xy-y2 For N=xy2-2x2y∂M∂y=y2-4xy…

Q: dx S- x4 - 1

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Q: 3- x 3) dx → S2xe* dx

A: To evaluate the given integrals.

Q: x2 - 10x - 5 dx J (x - 1)2(x² + 1)

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Q: 4x2-5х+6, 3. S(*-*+*)d *“)dx x2

A: We have two types of integrals in general, namely definite and indefinite integrals . The definite…

Q: 5- (2xe" + e')dx + (x² + 1)e³dy = 0

A: solving given DE by separation of variables.

Q: dx 1) S- x2-2x+1

A: As per the guidelines we can only solve one question post other question seperately. Formula used  ∫…

Q: 1 (x2 - y2) 3 dx

A: We have to evaluate ∫1x2-y232dx Let x=y secu Then: dxdu=dduy secu⇒dxdu=y secutanu⇒dx=y secutanu du…

Q: V -dx x² + 2

A: Given, I=∫xx2+24dx

Q: 2- (2xe + e*)dx + (x² + 1)e'dy = 0 %3D

A:

Q: 4. (2xe" + e*)dx + (x² + 1)edy = 0.

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 13. dx x5-3

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Q: ľ V2x + I dx S" x e*-1 dx

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Q: 2x Evaluate dx using suitable technique. (x² +4)(2x-1)

A:

Q: Evaluate:

A: Given integral is We know that

Q: 3. dx V3-x

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Q: 21 (b), dx -1 3e2x

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Q: dx 2. x2 – 6x + 13 -4 dx 3. (x – 2)3

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Q: x+3 k) S- dx x2+6x-11

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Q: X 2 dx = V4-x2

A: I=∫01x24-x2dx =∫01(4-x2)+44-x2dx =∫014-x24-x2dx+∫0144-x2dx =∫014-x2dx+4∫0114-x2dx Here  ⇒∫a2-x2…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.