Rewrite with x−1/2: Rewrite the integral with x to the power of −1/2. ∫26xx1dx=∫26x3/21dx
Pull out constant: Pull out the constant 261. ∫26x231dx=(261)∫x−23dx
Integrate x−23: Integrate x−23 with respect to x.(261)∫x−23dx=(261)(−12)x−21+C
Simplify expression: Simplify the expression.(\frac{\(1\)}{\(26\)})(\frac{\(-2\)}{\(1\)})x^{(-\frac{\(1\)}{\(2\)})} + C = (\frac{\(-2\)}{\(26\)})x^{(-\frac{\(1\)}{\(2\)})} + C
Reduce fraction: Reduce the fraction \(-\frac{2}{26} to −131.\left(-\frac{\(2\)}{\(26\)}\right)x^{-\frac{\(1\)}{\(2\)}} + C = \left(-\frac{\(1\)}{\(13\)}\right)x^{-\frac{\(1\)}{\(2\)}} + C
Rewrite as \(\frac{1}{\sqrt{x}}: Rewrite x−21 as x1. $\left(-\frac{\(1\)}{\(13\)}\right)x^{-\frac{\(1\)}{\(2\)}} + C = \left(-\frac{\(1\)}{\(13\)}\right)\left(\frac{\(1\)}{\sqrt{x}}\right) + C
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