∫du
∫du is the indefinite integral of the function du with respect to the variable u
∫du is the indefinite integral of the function du with respect to the variable u. The symbol ∫ represents integration, and du represents the differential of the variable u.
To find the value of the integral, you need to know the function du. If du is a constant value, the integral simplifies to u + C, where C is the constant of integration. For example, if du = 3, then ∫du = ∫3 d(u) = 3u + C.
However, if du represents a variable or a function of u, then you need additional information to evaluate the integral. In this case, you would need to know the specific function or relationship between u and du.
For example, if du is a function of u, such as du = 2u, then you can rewrite the integral as:
∫du = ∫2u d(u)
By applying the power rule for integration, which states that ∫x^k dx = (x^(k+1))/(k+1), you can integrate the function:
∫2u d(u) = (2u^(1+1))/(1+1) = (2u^2)/2 = u^2 + C
So, in this example, the integral of du, where du is equal to 2u, is u^2 + C, where C is the constant of integration.
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