What is the integral from 1 to e of (t^3+1)/t ?

The integral from 1 to e of (t^3+1)/t is (e^3-1)/3+1

Popular >

integral from 1 to e of (t^3+1)/t

\int_{1}^{e} \frac{t ^{3} + 1}{t} d t

\frac{e ^{3} - 1}{3} + 1

Decimal

7.36184 \dots

Solution steps

\int_{1}^{e} \frac{t ^{3} + 1}{t} d t

Expand

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

= \int_{1}^{e} t^{2} + \frac{1}{t} 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_{1}^{e} t^{2} d t + \int_{1}^{e} \frac{1}{t} d t

\int_{1}^{e} t^{2} d t = \frac{e ^{3} - 1}{3}

\int_{1}^{e} \frac{1}{t} d t = 1

= \frac{e ^{3} - 1}{3} + 1

\int_{0}^{π} cos^{2} (x) \cdot sin (x) d x

\int_{0}^{2} (2 x - 3) (4 x^{2} + 7) d x

\int_{- 0.5}^{0.5} 12 x^{2} - 3 d x

\int_{0}^{1} 14 x^{3} 1 - x^{2} d x

\int_{0}^{1} 9 x e^{x} d x

What is the integral from 1 to e of (t^3+1)/t ?
The integral from 1 to e of (t^3+1)/t is (e^3-1)/3+1