Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

\(\int \frac{dx}{x^{2022}}\left(1+x^{2022}\right)^{\frac{1}{2022}}\) is equal to

Options:

\(\frac{1}{-2021}\left[1+\frac{1}{x^{2022}}\right]^{1-\frac{1}{2022}}+C\)

\(\frac{1}{2023}\left[1-\frac{1}{x^{2022}}\right]^{1-\frac{1}{2022}}+C\)

\(\frac{-1}{2023}\left[1+\frac{1}{x^{2022}}\right]^{1-\frac{1}{2022}}+C\)

None

Correct Answer:

\(\frac{-1}{2023}\left[1+\frac{1}{x^{2022}}\right]^{1-\frac{1}{2022}}+C\)

Explanation:

\(x^{n}\left(1+x^{n}\right)^{\frac{1}{n}}=x^{n+1}\left(1+\frac{1}{x^{n}}\right)^{\frac{1}{n}}\)