What is the integral of (6x^2+2/(x^2)+5) ?

The integral of (6x^2+2/(x^2)+5) is 2x^3-2/x+5x+C

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integral of (6x^2+2/(x^2)+5)

\int (6 x^{2} + \frac{2}{x ^{2}} + 5) d x

2 x^{3} - \frac{2}{x} + 5 x + C

Solution steps

\int 6 x^{2} + \frac{2}{x ^{2}} + 5 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 6 x^{2} d x + \int \frac{2}{x ^{2}} d x + \int 5 d x

\int 6 x^{2} d x = 2 x^{3}

\int \frac{2}{x ^{2}} d x = - \frac{2}{x}

\int 5 d x = 5 x

= 2 x^{3} - \frac{2}{x} + 5 x

Add a constant to the solution

= 2 x^{3} - \frac{2}{x} + 5 x + C

\int e^{t} \frac{1}{t} d t

\int (x^{2} - sec^{2} (x)) d x

\int e^{x} (2 x - 1) d x

\int 2^{x} \cdot 5^{x} d x

\int (x - 1)^{3} d x

What is the integral of (6x^2+2/(x^2)+5) ?
The integral of (6x^2+2/(x^2)+5) is 2x^3-2/x+5x+C