Question

3√xdx

Answer 1

3√xdx
3√dx²
3.x√d
3x√d

Answer 2

It looks like you're asking about the integral of the function \(3\sqrt{x}\) with respect to \(x\). The expression can be written as:

\[
\int 3\sqrt{x} \, dx
\]

To solve this integral, we can rewrite \(\sqrt{x}\) as \(x^{1/2}\). Thus, the integral becomes:

\[
\int 3x^{1/2} \, dx
\]

Now we can apply the power rule for integration, which states that:

\[
\int x^n \, dx = \frac{x^{n+1}}{n+1} + C \quad \text{for } n \neq -1
\]

In this case, \(n = \frac{1}{2}\), so \(n + 1 = \frac{3}{2}\). Therefore, we have:

\[
\int 3x^{1/2} \, dx = 3 \cdot \frac{x^{3/2}}{\frac{3}{2}} + C = 3 \cdot \frac{2}{3} x^{3/2} + C = 2x^{3/2} + C
\]

Thus, the integral is:

\[
\int 3\sqrt{x} \, dx = 2x^{3/2} + C
\]

where \(C\) is the constant of integration.