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

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

Popular >

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

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

\frac{3 x ^{4}}{4} + ln ∣ x ∣ + C

Solution steps

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

Expand

x^{2} (3 x + x^{- 3}) : 3 x^{3} + \frac{1}{x}

= \int 3 x^{3} + \frac{1}{x} 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 \frac{1}{x} d x

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

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{3 x ^{4}}{4} + ln ∣ x ∣

Add a constant to the solution

= \frac{3 x ^{4}}{4} + ln ∣ x ∣ + C

\int sin (- 3 x) d x

t \to π lim (- 9 sin (- \frac{t}{2}))

\int - 3 x + 4 x d x

x^{- \frac{3}{4}}

\int_{0}^{\frac{π}{6}} (9 sec^{2} (x)) d x

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