Question

find integration
dy/(2y+3)²​

Answer 1

Step-by-step explanation:

Here a1=1,b1=2 ∴a1b1=12a1=1,b1=2 ∴a1b1=12

a2=2,b2=1 ∴a2b2=2a2=2,b2=1 ∴a2b2=2

Now, a1b1≠a2b2a1b1≠a2b2

Thus case - I applies, we have setting,

x=u+hy=v+k}x=u+hy=v+k}

dvdu=(u+2v)+(h+2k−3)(2u+v)+(2h+k−3)0dvdu=(u+2v)+(h+2k-3)(2u+v)+(2h+k-3)0

Choose h, k such that

h+2k−3=02h+k−3=0}h+2k-3=02h+k-3=0}

The solution is h = 1, k = 1

⇒dvdu=u+2v2u+v⇒dvdu=u+2v2u+v

Set