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

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

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

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

ln x^{2} + 1 - ln ∣ 2 + cos (x) ∣

Solution steps

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

Use the common integral:

\int \frac{1}{t} d t = ln (∣ t ∣)

= [ln ∣ t ∣]_{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}^{1} x^{4} (5 + 3 x^{5})^{4} d x

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

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

\int_{0}^{3} x^{2} e^{x} d x

\int_{\frac{π}{6}}^{\frac{π}{2}} cos^{2} (u) d u

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