Integration of 1/(ax+b)

Easy

100

Integrate 1/x

lnx + c

200

Integrate 1/(3x+1)

(1/3)ln(3x+1) + c

300

Integrate 5/(2-3x) 

-(5/3)ln(2-3x) + c

400

Integrate 4/(3-2x)
Upper bound = 3
Lower bound= 2

-ln9

500

Integrate 3/2(5x-1) 

3 ln(2x-5) + c

Medium

100

Integrate 1/(x+2)
Upper bound = 5
Lower bound = 0

ln3.5

200

Integrate 3/(2x-7)
Upper bound = 2
Lower bound = 0

-1.5ln(7/3)

300

Integrate 2 + (5/3x-2)
Upper bound = 10
Lower bound = 4

12 + (5/3)ln(14/5)

400

Integrate (3/x) - 4/(2x-1)
Upper bound = 3
lower bound = 1

ln (27/25)

500

Integrate (6x²+5x)/(2x-5)
Upper bound: 1
Lower bound: 0

23/2 - 25ln(5/3)

Hard

100

4x/(2x-1) = 2+ (A)/(2x-1)
Find the value of  the constant A

2

200

Integrate 2x-1 + (4/2x+3)
Upper bound: 3
Lower bound: -1

4 + ln81

300

Integrate 4x/(2x-1)
Upper bound: 5
Lower bound: 1

8 + ln9

400

A curve is such that dy/dx = 2x + 3/(x+e).
Given that the curve passes through the point (e,e²), find the equation of the curve

y = x² + 3ln(x+e) - 3ln2e

500

y = 2/(x+3)
Upper bound: K
Lower bound: 1
Given that the  shaded region has area 4, find the value of K

4e^{2 -} 3