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Question

I=3x+4x2+6x+5dx

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Solution

I=3x+4x2+6x+5dx=3x+95(x2+6x+5)dx
(2x+1)dxx2+6x+55dx(x2+6x+5)
(A)(3x+9)dxx2+6x+5=3(x+3)(x2+6x+5)dx
(x2+6x+5)=P
(2x+6)dx=dp
2(x+3)dx=dp
A3dp2(p)32ln|p|+c32lnx2+6x+5+c
(B)5dx(x2+6x+5)=5dx(x+3)245dx(x+3)2(2)2
x+3=p
dx=dp
B5dpp222
5dp[1(p+2)(p2)]54dp[1(p2)1(p+2)]
54ln|p2|54ln|p+2|54lnp2p+2
I=AB=32lnx2+6x+554lnp2p+2+c
3x+4x2+6x+5dx=32lnx2+6x+554lnp2p+2+c
=32lnx2+6x+554x+1x+5+c

1108507_1189637_ans_67509332dd4c40e99037a233ca6299db.jpeg

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