## Problem Statement

Calculate the definite integral:

$$
\int_{-1}^{0} \frac{\tan(x+1)}{\cos^2(x+1)} \, dx
$$
## Solution

$$
\begin{aligned}
& \int_{-1}^{0} \frac{\tan(x+1)}{\cos^2(x+1)} \, dx = \int_{-1}^{0} \tan(x+1) \cdot d(\tan(x+1)) = \left. \frac{\tan^2(x+1)}{2} \right|_{-1}^{0} = \\
& = \frac{\tan^2(0+1)}{2} - \frac{\tan^2(-1+1)}{2} = \frac{\tan^2 1}{2} - \frac{\tan^2 0}{2} = \frac{\tan^2 1}{2} - \frac{0^2}{2} = \frac{\tan^2 1}{2}
\end{aligned}
$$

Source — "http://pluspi.org/wiki/index.php/\�\�\�\�\�\�\�\�\�\�\�\� \%D0\%9A\%D1\%83\%D0\%B7\%D0\%BD\%D0\%B5\%D1\%86\%D0\%BE\%D0\%B2_\%D0\%98\%D0\%BD $\% \mathrm{D} 1 \% 82 \% \mathrm{D} 0 \% \mathrm{~B} 5 \% \mathrm{D} 0 \% \mathrm{~B} 3 \% \mathrm{D} 1 \% 80 \% \mathrm{D} 0 \% \mathrm{~B} 0 \% \mathrm{D} 0 \% \mathrm{BB} \% \mathrm{D} 1 \% 8 \mathrm{~B} \_4-24$ "

Categories: Kuznetsov Problem Book Integrals Problem 4 | Integrals

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## Problem Kuznetsov Integrals $4-25$

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