Please solve int(3x^5-2/x^3)dx?

Question

$int(3x^5-2/x^3)dx$

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Answer 1 · 2018-04-12T08:08:03

$I=1/2x^(6)+x^(-2)+C$

We want to integrate

$I=int3x^5-2/x^3dx=3intx^5dx-2intx^-3dx$

Remember the power rule for integration

$color(blue)(intx^ndx=(x^(n+1))/(n+1)+C$

Thus, by the power rule

$I=(3x^(5+1))/(5+1)-(2x^(-3+1))/(-3+1)+C$

$color(white)(I)=(3x^(6))/(6)-(2x^(-2))/(-2)+C$

$color(white)(I)=1/2x^(6)+x^(-2)+C$