What is the integral of (1+2t^3)/t ?

The integral of (1+2t^3)/t is ln|t|+(2t^3)/3+C

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integral of (1+2t^3)/t

\int \frac{1 + 2 t ^{3}}{t} d t

ln ∣ t ∣ + \frac{2 t ^{3}}{3} + C

Solution steps

\int \frac{1 + 2 t ^{3}}{t} d t

Expand

\frac{1 + 2 t ^{3}}{t} : \frac{1}{t} + 2 t^{2}

= \int \frac{1}{t} + 2 t^{2} d t

Apply the Sum Rule:

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

= \int \frac{1}{t} d t + \int 2 t^{2} d t

\int \frac{1}{t} d t = ln ∣ t ∣

\int 2 t^{2} d t = \frac{2 t ^{3}}{3}

= ln ∣ t ∣ + \frac{2 t ^{3}}{3}

Add a constant to the solution

= ln ∣ t ∣ + \frac{2 t ^{3}}{3} + C

\frac{\partial}{\partial x} (2 e^{2 x})

f (x) = x (x^{3} + 2 x + 3)

y^{^{''}} = a^{2} y

\int \frac{18}{x ( x ^{2} + 4 ) ^{2}} d x

4 - x, - 2, 6

What is the integral of (1+2t^3)/t ?
The integral of (1+2t^3)/t is ln|t|+(2t^3)/3+C