Q: Find the antiderivative of: x*+1 (n+ 1)2 [(n + 1) In x – 1] if n± -1 x* In x dx = z (In x)² + c if n…
A: Find the anti derivative.
Q: dy will be dx In x+1 If y = then 2x3 - 3x' (2x- 3x) +1)- (In x+ 1)(6x? – 3) (2x – 3x)? A. (2x - 3x)…
A: To find the dy/dx of the given function
Q: 10. Evaluate the integral. dx x²/4 – x²
A:
Q: |(In 6x)2 dx ОА. x(In 6x)2 - x(In 6x) + x + C В. x(In 6x)2 + 2x(In 6x) - 2x + C с. x(In 6x)2 - 2х(In…
A:
Q: 14. Evaluate the integral. 4 (y - 2)(2y + 1) dy
A: Given that : The integral is ∫04 ( y - 2) ( 2y +1) dy
Q: 19) * (xy)* = e ; f ind y' y' = [1+ In(xy)I y' = -y [1+ In Option 2 O Option 4 y' = [1- In(x None of…
A:
Q: x² + 2x- 10 (2x+4)+ 1) Consider dx evaluate x² (x² + 4x+ 5) (2x+4) + 1) dx- x2 + 4x +5) x2 x2 + 4x+5…
A: We want to evaluate the integral ∫2x - 2x2 - (2x+4)+1x2+4x+5dx
Q: EXAMPLE 7 If it is known that f(x) dx = 12 and f(x) dx = 10, find f(x) dx. SOLUTION By a property of…
A: We have to solve
Q: 2+3x-7) X-2 dx Evaluate the integral: Se A²+ +In|3x-6|+C Ⓡ 1/²/₁ 2²+5x+! In/x-21 +C B 3 x²+5x+In…
A:
Q: Find the antiderivative of: xn+1 [(n + 1) In x – 1] if n+ -1 x" In x dx = (n + 1)² 1 (In x)² + C 2…
A:
Q: In x Evaluate S 2 x(4-ln² x) O2 ln | 4 - In² x | +C Oln | 4 - ln² x | +C O ln | 4 - In² x | +C Onx…
A: Given ∫lnxx4-ln2xdx
Q: The integral S.¹0 d 10 x²+6 x-8 is improper. dx
A: The given integral is (x2+6)/(x-8) , limit from 6 to 10.
Q: x2 dx (x– 1)3 1 In|x-1|- X-1 + C 2(x– 1)? 2 In|x-1| 1 +C 2(x – 1)2 X-1 2 In|x-1|- X-1 1 O Inlx- +C…
A:
Q: In|In x| + C 2.STinx dx x In x 1 3/x +C 3. S dx
A:
Q: 1. Evaluate S xe0.1% dx In x 2. Evaluate Sdx x3 3. Evaluate S x³(x² – 1)1°dx | 4. Evaluate (2 +…
A:
Q: Evaluate √x² + x + 2 dx x²-1 x+1 In: +C (x-1)² 0₁ (x-1)² In- + C x+1 O x + 1 (x-1)² (x-1)² x+1 X+…
A: Solution is here
Q: (2x+4) + 1 x² +2x- 10 dx = x² (x² + 4x +5) (2x +4) +1) dx- x² + 4x+5, Consider dx evaluate | x² + 4x…
A:
Q: 12. Find the integral of S (x². √(x² + ² =) dx
A:
Q: 9. Evaluate the integral: dx |2x² +1 - In /2.x +1 + C c. (2. +1) +C -2x +1 +C D. x In2x +1 +C В.
A: Please see the explanation below
Q: In x /1+ (In x)² 6 S -dx
A: Given query is to eveluate the integral.
Q: 1. Evaluate these: 1 -x* +c dx *dx (i) x'd< (Ans. x² +c J; (iii) |xdx dx (Ans. ); (ii) (Ans. 2 5 );…
A:
Q: 2. * S arctan x dx 1 In(x²) + C C 1. x arctan x C A x arctan x -In(x² + 1) + C -- B 1 D x arctan x…
A: Solve the given integration
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: 3. f(x) = -x² +1 Ex)(+x). x2 + x - 6 %3D Holes: Vert. Asy: Hor. Asy:
A: Now plotting the graph of given function we get :
Q: хах 11. The integral f 4-х2 is equal to 1 A. In | | + C C.-글m14- x리 + C 4 x+2 2+x B. In |4 – x2|+C…
A:
Q: x² + 2x- 10 (2 dx = x² (x² + 4x + 5) (2x + 4) + 1) (2x+ 4) +1) x2 + 4x + 5 x2 2 Consider dx -…
A:
Q: de xdx 1. (In* 4x-1) 2. V3x +5 sin 4x de de 4. 9+8cos 2x 3. (5x-3)dr 5. 3x-3x+2 (3-4x)dx 6. TAx…
A:
Q: 2. Integrate: x² In x dx a. In x+c. b. [(In x)² ++c c. [(Inx)² - Inx+]+c d. none of these
A: The given integral is x2lnx.
Q: 2. Find the integral 2x+3 dx x2-9 a. In/(x – 3)³(x + 3) + C а. b. In[(x – 3)³(x + 3)] +C c. 2ln[(x –…
A:
Q: Г. 5 1, г)ах — 9, g(x)dx 8 Compute: -[о g(x)dx b.) == 5 3f(х)dx %— с.) .5 f(x)dx d.) 2 "/Г 5…
A: Given,
Q: 3+ Evaluate the integral: Se³+ cosh2x33+ cosh2xsinh2x dx (3e)³ 3+ sinh2x A + C 21n3 (3e)3 + sinh2x B…
A: Application of integration
Q: 12. Evaluate the integral. x² – 4 – dx
A:
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…
A:
Q: 8) F(s)=³-ks² 2 Ans. f(1) =2(e"-1)-! k
A: Solve the following
Q: 6. Evaluate the integral dx (4x2 + 1)(x² + 4)
A:
Q: 12 Sf x² ydxdy 01 In2 2 11₂ SS 2xe dxdy 0-1 3 1 2xy SS- -dxdy 10x+1 4√x 2 S S x²y dydx 00 11-y S S…
A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…
Q: (1 + 1 1 + In(x) + - X (x+y)ln(x) - 5y = c dx = (5-In(x)) dy
A:
Q: 8. The value of the integral 2[x] 1o sulsV ar 3x-[x] dx, where [] denotes the greatest integer 2[x]…
A:
Q: In Evaluate the integral: Sé e x²+3x-7 x-2 dx
A: Option (b) x22+5x+3ln|x-2|+C
Q: 8. Evaluate the integrals. * Sx³ (x² + 1)5 dx
A:
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: S √x²-a² X dx
A: To solve the given integral.
Q: 9. dx 1+ ex A - In le *|+ C C - In le x +1 + C %3 In leI+ C B D Inle x+11+ C x- O D O E None
A:
Q: x²+3x-7 X-2 +5x+31n|x-2|+C + +In|3x-6|+C 2 x²+5x+In/3x-6|+C x² + 5x + n/x-21 +C 2 3 In Evaluate the…
A:
Q: 5. prove that d (-x) (+ x) = X dx dx d² dx² - x² +1
A:
Q: 7. Evaluate the integral x4 6x5 1 dx
A:
Q: 3+ Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx (3e)3+ sinh2x A +C 2+In3 (3e)3 + cosh2x +C…
A:
Q: In ( x² + 3x -=-7) dx X-2 Evaluate the integral: Se Ⓒ + A x² 2 =+ + In|3x-6|+C ℗ +² +5x+3n|x-2/+C B…
A: To find out the integration.
Q: 2x²-3x + 10 dx (x²+4)2
A: The objective of the question is evaluate the indefinite integral.
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- One leukemic cell in an otherwise healthy mouse will divide into two cells every 12 hours, so that after x days the number of leukemic cells will be f(x) = 4x. (a) Find the approximate number of leukemic cells after 12 days. ________ cells (b) If the mouse will die when its body has a billion leukemic cells, will it survive beyond day 14? Yes or NoSuppose that a construction zone can allow 50 cars per hour to pass through and that cars arrive randomly at a rate of X cars per hour. Then the average number of cars waiting in line to get through the construction zone can be estimated by: N(x)=x2/2500-50x Evaluate N(20), N(40), and N(49).Explain what happens to the length of the line as X approaches 50.If the average number of cars waiting in line is 1, find the average of cars per hour.Find and interpret the vertical asymptotes.why wouldnt it be 0.10 since its larger than 0.5?
- Evaluate integral x^3+x+2/x^2+2x-8Find integral fraction (numerator) y dy / (denominator) square root of (y+2) using the substitution u + 5 = square root of (y+2)A drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by S = 40x19/7 − 560x12/7 + 1960x5/7 where x is in hours and 0 ≤ x ≤ 7. Find the average number of milligrams of the drug in the bloodstream for the first 7 hours after a capsule is taken. (Round your answer to the nearest whole number.)