Question

Indefinite Integrals using Basic Rules of Integration

Answer 1

\[\int\limits \frac{ x ^{4} +2x ^{2} +1 }{ x ^{2} }\]

Answer 2

*dx

Answer 3

Glad you remembered that 'dx.'

Hint: break this integral into three separate integrals. In the first two cases, reduce the fraction. In the third case, use a negative exponent to represent 1/ (x^2).

Answer 4

\[\int\limits x^4 + \int\limits 2x ^{2} + \int\limits 1\]you mean like

Answer 5

and I integrate each one? @mathmale

Answer 6

Givanna: what happened to your denominator, x^2? Also, what happened to "dx?"
Yes, integrate each integral separately and then add the results together with just one constant of integration, C.

Answer 7

So your first (of three) integrals will be Int [(x^2)dx ].

Answer 8

\[\int\limits \frac{ x^4 }{ x^2 } dx + \int\limits \frac{ 2x ^{2} }{ x^2 } dx + \int\limits \frac{ 1 }{ x^2 } dx\]

Answer 9

\[\int\limits x^2 dx + \int\limits 2 dx + \int\limits x^-2 dx\]

Answer 10

\[\frac{ x^3 }{ 3 } + 2x - \frac{ 1 }{ x } +c\]

Answer 11

@mathmale

Answer 12

Surely looks good!
If you want to check your answer, differentiate all four terms. Combine the results using the LCD.