Question

Find the indefinite integral. 6dx\int 6 d x

Solution

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Let us calculate 6dx\displaystyle\int{6\,dx}.

6dx=Rule16dx=6x+C\begin{align*} \int{6\, dx}&\overset{\footnotesize{Rule\,1}}{=} 6\cdot \int{\,dx}\\ &\quad=6\cdot x +C \end{align*}

Where Rule\textbf{Rule} 1\pmb{1} is given by

kdx=kx+C\boxed{\int{k\, dx=k\cdot x+C}}

(kk, a constant).

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