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

The integral from 2+cos(x) to x^2+1 of 1/x is ln|x^2+1|-ln|2+cos(x)|

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int_{2 + c o s (x)}^{x^{2} + 1} \frac{1}{x} d x

ln x^{2} + 1 - ln ∣ 2 + cos (x) ∣

Solution steps

\int_{2 + c o s (x)}^{x^{2} + 1} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= [ln ∣ x ∣]_{2 + c o s (x)}^{x^{2} + 1}

Compute the boundaries:

ln x^{2} + 1 - ln ∣ 2 + cos (x) ∣

= ln x^{2} + 1 - ln ∣ 2 + cos (x) ∣

\int_{0}^{4} x x^{2} + 3 d x

\int_{0}^{1} (x^{2} + 4) e^{3 x} d x

\int_{0}^{4} x x^{2} + 6 d x

\int_{0}^{1} x^{2} (2 + 2 x^{3})^{5} d x

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

What is the integral from 2+cos(x) to x^2+1 of 1/x ?
The integral from 2+cos(x) to x^2+1 of 1/x is ln|x^2+1|-ln|2+cos(x)|