Integrate!

Calculus Level pending

$\large \int a^{\ln x} \, dx$

Find the indefinite integral above for constant $a$ .

Ignore all arbitrary constants of integration .

\frac{x^{\ln({a}+x)}}{\ln({a}+x)}

\frac{x^{\ln({a})+1}}{\ln({a})+1}

\frac{x^{\ln({a}+1)}}{\ln({ a}+1)}

\frac{\text{a}^{\ln({a}+x)}}{\ln({a}+1)}

1 solution

Yasir Soltani
Jun 12, 2016

Note that $\text{a}^{\ln(x)}= x^{\ln(a)}$ therefore

$\begin{aligned} \int \text{a}^{\ln(x)} \text{d}x &=\int x^{\ln(a)} \text{d}x \\ &=\frac{ x^{\ln(\text{a})+1}}{\ln(\text{a})+1} \quad (\text{C}=0)\\ \end{aligned}$

Integrate!

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