e2 dx 2x (In x)3 e

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

A:

Q: x'e-2x dx 20 dx 2

A:

Q: 2x dx e2* +3e" +2 5.

A: To solve this integral, a substitution of is taken. Then it is differentiated to find the value of…

Q: S (x² + 1) e~3* dx -3x

A: we have to simply compute the following integral

Q: (4x3-6х) dx 3. S x*-3x²+2

A: ∫4x3-6xx4-3x2+2dx we know that∫f'(x)f(x)dx = ln|f(x)| +cf'(x) =4x3-6x , f(x)=x4-3x2+2

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: 52. x"e*dx = x"e* -nfxle*dx

A:

Q: 3. dx (x²+1)² -3 d x XVX +3, dx x2

A: Evaluate the given integrals

Q: e2 dx 2x (In x)3 e

A: Given:

Q: x2 dx l-x²

A: Given:      I=∫x21-x2dx     put x= sin t    ⇒ t= sin-1x          dx=cos t dt     I=∫sin2…

Q: e そo 3/2 S-スス)ん dx (4x²+1)-

A: We have to find the value of the integral  ∫(1-x2)3/2x6dx Note- since you have posted multiple…

Q: e2 6. - dx -Find 1

A:

Q: 3-S(1+ x²)e=*dx

A:

Q: 12. S e 3In(2x-1) 2x - 1 - dx

A: The given integral is: I=∫e3ln2x-12x-1dx   As we know the Power Rule: ∫ax+bndx=ax+bn+1an+1+C

Q: e2 1 dx x In x e

A:

Q: 3(x5 + x³) ez"+xª + 3(x6 +xª) +2 dx -2

A:

Q: e2x +2e* dx e* +1

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Q: 19. (E x' 3) dx

A: #19 Differentiation w.r.t. x

Q: V1+x3 dx [6] S (7) (ax2a (x2a+1)*dx x-2 ах2а (7] S

A: Given: (1)   ∫1+x33x-2dx (2)  ∫ax2ax2a+13xdx

Q: 2X 2x -ë dy+2lyê¯-x) dx =e

A:

Q: 20. e ³.x (e²x + 1)² dx

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Q: • S (++:) (- 1 x2 – 1 dx - x2

A:

Q: PO 5.5. -X².11+ y²) xe dx dy

A:

Q: 2 4 E (x² + 2)V4 – x² dx 3

A: Let's find.

Q: 3x dx e 6. 1+ еx

A: Compute the value of the given integral ∫e3x1+exdx as follows. Let u=1+ex, then ex=u-1 Now…

Q: 6) e2*dx +?ydy = e²*dx +ydy – 2dy + eln(x)dx

A:

Q: x19 e2x' e'dx x19 e2x° e1dx -1

A: The solution of integral

Q: cosh x dx е e- 2х

A: Given integral is ∫coshxe-2xdx

Q: d. 2x³ + 1 x4 + 2x 12x -dx h. 1 ²x² - 2x + 1 x² dx

A:

Q: e-k* xn-1 dx ,n > 0 k> 0

A:

Q: 1. X-6 dx x2 – 6x + 8 Jo

A: I have provided solution in step2

Q: e2x 4. dx e2a + 3e + 2

A:

Q: (a) f(x) dx = Enter an exact number only. 4 (b) |(4f(x) + 10x)dx = Enter an exact number only. 4

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Q: 3. f(e-²x - 1) dx

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Q: e2x dx V1 + e*

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Q: s e8*(x³ + x²)sec² (x*e3* + 1) dx

A:

Q: e¬*dx 4 + e-2x

A:

Q: 6:B:Find the general solution of: +9 0 dx dx2

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Q: e* - x e* et dx = 2x2 + constant 2 х

A: To show that∫ex-xex2x2dx=-ex2x+constant

Q: e2x 4. dx e2r + 3e + 2

A: We can evaluate the given integral by using the substitution u = ex  and the following equation.…

Q: a. S(x² – 1)e*²-3x dx

A:

Q: 4 2 + e )dx y2 x =

A:

Q: A ) Find ∫ dx / a2 + x2 B ) Find ∫ x2 + √x - √2 dx C ) Find ∫ x2e-x dx

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 2 – x² /4 dx e

A: Here we the formula ∫2e-x2πdx =erf(x)  it is gauss error function}

Q: 2 2e* dx e3x + e* 3 2 dx (x + 1)²

A:

Q: 3. S(3+*+6 – e2*)dx 4. S 2x3e**dx xp,

A:

Q: 20. (x² + 1)e¯* dx

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Q: 6 dx = x2 + x-2 21n I +2 * -1

A:

Q: x² + 3x – 44 c. -dx (x+3)(x+5)(3x – 2)

A: Given integral

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.