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Question 15

\begin{align} \int\sqrt {x}.\left(3x^2+2x + 3\right).dx\end{align}

Answer
\begin{align} \int\sqrt {x}.\left(3x^2+2x + 3\right).dx\end{align}
 
\begin{align} =\int\left(3x^\frac52+2x^\frac32 + 3x^\frac12\right).dx\end{align}
 
\begin{align} =3\int x^\frac52 .dx+2 \int x^\frac32 .dx + 3\int x^\frac12.dx\end{align}
 
\begin{align} =3\left(\frac{x^{\displaystyle\frac72}}{\displaystyle\frac72}\right) + 2\left(\frac{x^{\displaystyle\frac52}}{\displaystyle\frac52}\right)+3\left(\frac{x^{\displaystyle\frac32}}{\displaystyle\frac32}\right)+C \end{align}
 
 \begin{align} =\frac67\;x^\frac72\; + \frac45\;x^\frac52\;+ 2x^\frac32\; +C \end{align}
 

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