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 BExplanation:Let I=∫2x2+5x9(x5+x3+1)3dx =∫2x12+5x9x15(1+x−2+x−5)3dx =∫2x−3+5x−6(1+x−2+x−5)3dx Now put 1+x-2+x-5=t ⇒(−2x−3−5x−6)dx=dt ⇒(2x−3+5x−6)dx=−dt ∴I=−∫dtt3=−∫t−3dt =−t−3+1−3+1+C=I2t2+C x102(x5+x3+1)2+C