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Black Advanced Problems in Mathematics

Exam: Black Advanced Problems in Mathematics
Subject: Mathematics
Chapter: Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

∫ ( (x^2 - x + 1)/(x^2 + 1) ) e^ ^ -1 (x) dx = f(x) · e^ ^ -1 (x) +...

\int \left( \frac{x^2 - x + 1}{x^2 + 1} \right) e^{\cot^{-1}(x)} dx = f(x) \cdot e^{\cot^{-1}(x)} + C

where

C

is constant of integration. Then

f(x)

is equal to :

Options

A $-x$
B $\sqrt{1-x}$
C $x$
D $\sqrt{1+x}$

Correct answer

C. $x$

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