What is the integral from pi to 2pi of (1+cos(x))/x ?

The integral from pi to 2pi of (1+cos(x))/x is ln(2)+\Ci(2pi)-\Ci(pi)

Popular >

integral from pi to 2pi of (1+cos(x))/x

\int_{π}^{2 π} \frac{1 + cos ( x )}{x} d x

ln (2) + Ci (2 π) - Ci (π)

Solution steps

\int_{π}^{2 π} \frac{1 + cos ( x )}{x} d x

Expand

\frac{1 + cos ( x )}{x} : \frac{1}{x} + \frac{cos ( x )}{x}

= \int_{π}^{2 π} \frac{1}{x} + \frac{cos ( x )}{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_{π}^{2 π} \frac{1}{x} d x + \int_{π}^{2 π} \frac{cos ( x )}{x} d x

\int_{π}^{2 π} \frac{1}{x} d x = ln (2)

\int_{π}^{2 π} \frac{cos ( x )}{x} d x = Ci (2 π) - Ci (π)

= ln (2) + Ci (2 π) - Ci (π)

\int_{\frac{1}{10}}^{\frac{11}{10}} \frac{1}{x} d x

\int_{4}^{5} \frac{1}{( y - 4 ) ^{\frac{1}{3}}} d y

\int_{1}^{4} (e^{3 x} - \frac{1}{x}) d x

\int_{0}^{1} x 7^{x} d x

\int_{0}^{\frac{3 π}{2}} 2 + 2 sin (x) d x

What is the integral from pi to 2pi of (1+cos(x))/x ?
The integral from pi to 2pi of (1+cos(x))/x is ln(2)+\Ci(2pi)-\Ci(pi)