32 8y%dy y-15 2.

Q: s(VE + E dx

A: We want to integrate the given function.

Q: 17 5. S dx х2+ 13х +1

A: We can use the following standard integration result to evaluate the given integral:…

Q: 14 Lys 9 -25+ dy = Vy

A:

Q: 3y+125 dy (e+5)² Зу

A: we need to evaluate the given indefinite integration

Q: dx dy 26.

A:

Q: 2. S(2 – 3e*) dx

A:

Q: 2. | csch´x coth x dx

A:

Q: 8y3–1 dy 5. S 2у+1

A:

Q: 00 e-2y dy 0.

A:

Q: 1 (2x-3)4 4. S dx

A: Follow the procedure given below.

Q: 2х+3 3. S ·dx (х+1)(x2+4)

A: We have to find the given integral. We will use partial fraction decomposition. We know that-…

Q: S(x + 3)e*+6x dx

A:

Q: 25y2-4 dy 415 S. 2/5

A: ∫254525y2-4y dy Put, y=25secθ Differentiating with respect to θ, we get ⇒dydθ=25secθ tanθ⇒dy=25secθ…

Q: 6y dx dy

A: x limit  x=y2and y is from 0 to 1 Option B

Q: S (28*_ 4 e²_ 1) 2) dx |

A:

Q: 5 6 7 | || ? +y² +²) dx dy e -5 0 0

A: Given: ∫-55∫06∫07x2+y2+z2dxdydz

Q: 2 / y xx lnx xy + y = In

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: cln /3 2e" Ve2x +1 dx

A:

Q: dx/lny+dy/x^2-0 ; y(3)= 1 and  y(3)=-1

A: The solution of above differential equation is written below.

Q: 5.5 dy √y.evy 6. Š dx X+ e 7. fete d dx 8. fdx

A: Here we have to find the integral.

Q: 2) 3. | 24 ly-11 dy

A:

Q: 6 S(3csc°C+) - &e*)dt

A: Given integration is : ∫3 cosec2t-8et dt To find the value of integration

Q: 8. ylnx – x In y = c - 9. y = ln (coth x) 10. y = sec³Vx

A:

Q: de (iv) x(y² – 1) + y(x² + 1) dx

A:

Q: х(3ху — 4у3 + 6)dx + (x3 — бх?у — 1)dy — 0

A: A differential equation of the form Mdx+Ndy=0 is said to be exact differential equation if it…

Q: b. S dx ¿ -1

A:

Q: (4) S xe*dx xe* + e* + c ex — хе* + с Option Option 2 хе* — ех + с Option 3

A:

Q: 12х-4 3. S dx 2х-1

A:

Q: 5. (y -x')dx+xydy = 0

A:

Q: e3x dx ex – 1

A: Given: I=∫e3xex−1dx

Q: 3 ln x + 2 ln y − 4 ln z

A: To simplify: 3lnx+2lny-4lnz Solution: 3lnx+2lny-4lnz On simplifying further we get:…

Q: x^2(lnx-lny)dy=y(ylny-ylnx)dx

A: Explained below

Q: 7. If S PCx) dx = 14 and %3D S.I find 6. fCx)dx

A:

Q: Find dy/dx

A: the given expression is: y=∫0x1+t2dt we have to find the value of dydx

Q: 4. S(x + e*)²dx

A: ∫x+ex2dx

Q: •4 (ii) 2y dy dx.

A:

Q: 2 S dz = 3. S dv

A:

Q: dy 9ху — 5у dx

A:

Q: 12.) S³ S² (3x - 2y ¹) dy dx

A: according to company rules we can answer only the first question and rest can be reposted.

Q: Eveluet I= dx dy I+x'ダノ Cali calia い

A: The given integral is: I=∫02∫y4-y2 11+x2+y2 dx dy

Q: dy 1+y+1

A:

Q: 24. Evalute dx r +1

A: Given: ∫0∞x12x3+1dx

Q: S 3 Lnx+1 XLn x-2x .dx

A:

Q: S 3e-5" dx

A:

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

A:

Q: Gy-5 (ay +1)3 dy

A: ∫6y-5(3y+1)2dy

Q: 9. S(9 + 8y – y²)? dy 10. S (e*–2)² dx e 2x + 4

A:

Q: 8. S Ve3x dx A 3 3 2x e3* + C 2. 2 e2* + C 3 B e 3x. e* + C

A:

Q: ∫(e^y dy)/(e^y-1)

A: Given, ∫eydyey-1