What is the integral of (3x^3+4x^2-2x^{-1}+13) ?

The integral of (3x^3+4x^2-2x^{-1}+13) is (3x^4)/4+(4x^3)/3-2ln|x|+13x+C

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integral of (3x^3+4x^2-2x^{-1}+13)

\int (3 x^{3} + 4 x^{2} - 2 x^{- 1} + 13) d x

\frac{3 x ^{4}}{4} + \frac{4 x ^{3}}{3} - 2 ln ∣ x ∣ + 13 x + C

Solution steps

\int 3 x^{3} + 4 x^{2} - 2 x^{- 1} + 13 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 3 x^{3} d x + \int 4 x^{2} d x - \int 2 x^{- 1} d x + \int 13 d x

\int 3 x^{3} d x = \frac{3 x ^{4}}{4}

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int 2 x^{- 1} d x = 2 ln ∣ x ∣

\int 13 d x = 13 x

= \frac{3 x ^{4}}{4} + \frac{4 x ^{3}}{3} - 2 ln ∣ x ∣ + 13 x

Add a constant to the solution

= \frac{3 x ^{4}}{4} + \frac{4 x ^{3}}{3} - 2 ln ∣ x ∣ + 13 x + C

t^{2} cos (5 t)

\frac{sin ( x )}{2 + cos ( x )}

sin (5 x), x = 0

\frac{1}{ln ( x + 1 )}

\frac{\partial}{\partial y} (5 x + y)

What is the integral of (3x^3+4x^2-2x^{-1}+13) ?
The integral of (3x^3+4x^2-2x^{-1}+13) is (3x^4)/4+(4x^3)/3-2ln|x|+13x+C