∫2x4x−x2 dx=∫(2x31−2x21)dx=21∫x31 dx−21∫x21 dx Now solving: ∫x31dxApply power rule:∫xndx=n+1xn+1 with n=−3:=−2x21 Now solving:∫x21 dx Apply power rule with n=−2:=−x1 Plug in solved integrals:21∫x31 dx−21∫x21 dx=2x1−4x21 The problem is solved:=∫2x4x−x2 dx2x1−4x21+C Simplifying the above, we have:y=4x22x−1+C At y=2 when x=1, we have:
2=4(1)22(1)−1+C2=42−1+C2=41+C2−41=C⟹C=1.75∴y=4x22x−1+1.75
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