Question: \begin{align} \int \frac{x^3 + 3x + 4}{\sqrt{x}} . dx\end{align}

Answer:

\begin{align} \int \frac{x^3 + 3x + 4}{\sqrt{x}} . dx\end{align}

\begin{align} =\int \left(x^\frac{5}{2} + 3x^\frac{1}{2} + 4x^\frac{1}{2}\right) . dx\end{align}

\begin{align} =\frac{\left(x^{\displaystyle\frac72}\right)}{\displaystyle\frac72}+ \frac{3\left(x^{\displaystyle\frac32}\right)}{\displaystyle\frac32} + \frac{4\left(x^{\displaystyle\frac12}\right)}{\displaystyle\frac12} + C\end{align}

\begin{align} =\frac27\left(x^\frac72\right)+ 2\left(x^\frac32\right) + 8\left(x^\frac12\right) + C\end{align}

\begin{align} =\frac27\left(x^\frac72\right)+ 2\left(x^\frac32\right) + 8\left(\sqrt x\right) + C\end{align}

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Question: \begin{align} \int \frac{x^3 + 3x + 4}{\sqrt{x}} . dx\end{align}

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