What is the integral from 1 to e of (x^6+1)/x ?

The integral from 1 to e of (x^6+1)/x is (e^6-1)/6+1

Popular >

integral from 1 to e of (x^6+1)/x

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

\frac{e ^{6} - 1}{6} + 1

Solution steps

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

Expand

\frac{x ^{6} + 1}{x} : x^{5} + \frac{1}{x}

= \int_{1}^{e} x^{5} + \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^{5} d x + \int_{1}^{e} \frac{1}{x} d x

\int_{1}^{e} x^{5} d x = \frac{e ^{6} - 1}{6}

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

= \frac{e ^{6} - 1}{6} + 1

\int_{2}^{1} 1 d x

\int_{- π}^{0} sin (x) cos (n x) d x

\int_{0}^{\frac{π}{2}} sin^{2} (z) d z

\int_{1}^{5} \frac{z ^{2} + 3}{z} d z

\int_{0}^{7} 14 x - x^{2} d x

What is the integral from 1 to e of (x^6+1)/x ?
The integral from 1 to e of (x^6+1)/x is (e^6-1)/6+1