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1)

The intergral 2x12+5x9(x5+x3+1)3dx is equal to 

where C is an arbitrary constant


A) x5(x5+x3+1)2+C

B) x102(x5+x3+1)2+C

C) x52(x5+x3+1)2+C

D) x102(x5+x3+1)2+C

Answer:

Option B

Explanation:

Let I=2x2+5x9(x5+x3+1)3dx

=2x12+5x9x15(1+x2+x5)3dx

=2x3+5x6(1+x2+x5)3dx

Now put 1+x-2+x-5=t

(2x35x6)dx=dt

 (2x3+5x6)dx=dt

I=dtt3=t3dt 

=t3+13+1+C=I2t2+C

x102(x5+x3+1)2+C