What is the integral from 1 to e of (x^7+1)/x ?

The integral from 1 to e of (x^7+1)/x is (e^7-1)/7+1

Popular >

integral from 1 to e of (x^7+1)/x

\int_{1}^{e} \frac{x ^{7} + 1}{x} d x

\frac{e ^{7} - 1}{7} + 1

Solution steps

\int_{1}^{e} \frac{x ^{7} + 1}{x} d x

Expand

\frac{x ^{7} + 1}{x} : x^{6} + \frac{1}{x}

= \int_{1}^{e} x^{6} + \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_{1}^{e} x^{6} d x + \int_{1}^{e} \frac{1}{x} d x

\int_{1}^{e} x^{6} d x = \frac{e ^{7} - 1}{7}

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

= \frac{e ^{7} - 1}{7} + 1

\int_{1}^{5} 1 + \frac{1}{x} + \frac{1}{x ^{2}} d x

\int_{1}^{2} \frac{x - 3}{x} d x

\int_{0}^{4} 16 x - x^{3} d x

\int_{0}^{5} (x^{2} - x + 1) e^{2 x} d x

\int_{0}^{6} ∣ x - 5 ∣ d x

What is the integral from 1 to e of (x^7+1)/x ?
The integral from 1 to e of (x^7+1)/x is (e^7-1)/7+1