List of top Mathematics Questions on Indefinite Integrals asked in CUET (UG)

Match the LIST-I with LIST-II
LIST-I
Indefinite Integral		LIST-II
Solution (where \(c\) is an arbitrary constant)
A. \(\int\sqrt{16-x^2}\,dx\)I. \(\sin^{-1}\left(\frac{x}{4}\right)+c\)
B. \(\int\frac{dx}{\sqrt{16-x^2}}\)II. \(\frac{x}{2}\sqrt{16-x^2}+8\sin^{-1}\left(\frac{x}{4}\right)+c\)
C. \(\int\frac{dx}{\sqrt{x^2-16}}\)III. \(\frac{1}{8}\log\left|\frac{4+x}{4-x}\right|+c\)
D. \(\int\frac{dx}{16-x^2}\)IV. \(\log\left|x+\sqrt{x^2-16}\right|+c\)
Choose the correct answer from the options given below:
Find the value of: \[ \int \frac{1}{x} \, dx \]
Evaluate: \[ \int (3x^2 + 4x - 5) \, dx \]
Evaluate the indefinite integral using pattern-based substitution: \[ \int \frac{\ln x - 1}{(\ln x)^2}\,dx \]
Evaluate the indefinite integral: \( \int \frac{x^2+1}{x^4+1}\,dx \)
The integral \( \int e^x \left(\tan^{-1}x + \frac{1}{1+x^2}\right) dx \) is equal to
The integral \( \int \frac{2+x^4}{1+x^2} dx \) is equal to
The integral I = $\int \frac{e^{5\log_e x} - e^{4\log_e x}}{e^{3\log_e x} - e^{2\log_e x}} dx$ is equal to
If \(\int \frac{(1 + x \log x)}{xe^{-x}} dx = e^x f(x) + C\), where C is constant of integration, then f(x) is
The integral I = $\int e^x (\frac{x-1}{3x^2}) dx$ is equal to
The integral I = $\int \frac{e^{5\log_e x} - e^{4\log_e x}}{e^{3\log_e x} - e^{2\log_e x}} dx$ is equal to
The integral I = $\int e^x (\frac{x-1}{3x^2}) dx$ is equal to
If \(\int \frac{(1 + x \log x)}{xe^{-x}} dx = e^x f(x) + C\), where C is constant of integration, then f(x) is