Consider the following
I. `intlog10dx=x+C`
II. `int10^(x)dx=10^(x)+C`
Which of the above is/are correct ?

Options

A. Only I
B. Only II
C. Both I and II
D. Neither I nor II

Answer

To solve the question, we need to evaluate the two integrals provided and determine whether the statements are correct.

### Step 1: Evaluate the first integral \( \int \log_{10} x \, dx \)

1. **Recognize that \(\log_{10}\) is a constant**:
- Since \(\log_{10}\) is a constant (approximately 0.301), we can factor it out of the integral.

\[ \int \log_{10} x \, dx = \log_{10} \int dx \]

2. **Integrate \(dx\)**:
- The integral of \(dx\) is simply \(x\).

\[ \int dx = x \]

3. **Combine the results**:
- Thus, we have:

\[ \int \log_{10} x \, dx = \log_{10} x + C \]

4. **Compare with the given statement**:
- The statement given is \( \int \log_{10} dx = x + C \), which is incorrect. The correct result is \( \log_{10} x + C \).

### Step 2: Evaluate the second integral \( \int 10^x \, dx \)

1. **Use the formula for the integral of an exponential function**:
- The integral of \(a^x\) is given by:

\[ \int a^x \, dx = \frac{a^x}{\ln a} + C \]

- Here, \(a = 10\).

2. **Apply the formula**:
- Therefore, we have:

\[ \int 10^x \, dx = \frac{10^x}{\ln 10} + C \]

3. **Compare with the given statement**:
- The statement given is \( \int 10^x \, dx = 10^x + C \), which is incorrect. The correct result is \( \frac{10^x}{\ln 10} + C \).

### Conclusion
Both statements I and II are incorrect.

### Final Answer
Neither statement I nor II is correct.

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