Question

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

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

Answer 1

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

Explanation:

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`