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

$We have, \int e^{xln (a)} dx = \int e^{\ln {(a)}^{x}} dx = \int a^{x} dx = \frac{a^{x}}{\ln (a)} + c$

$\int_{0}^{\frac{π}{2}} |\sin (x) - \cos (x)| d x = ?$

$\int_{0}^{\frac{π}{2}} e^{\sin (x)} \cos (x) d x = ?$

$What is \int \ln (x^{2}) dx = ?$

$What is \int_{0}^{π} e^{x} \sin (x) d x = ?$

$What is \int_{1}^{e} xln (x) d x = ?$

$What is \int_{0}^{\sqrt{2}} [x^{2}] d x equal to (where [.] is the greatest integer function) ?$

$What is \int \frac{dx}{2^{x} - 1} = ?$

$What is the value of \int_{\frac{- π}{4}}^{\frac{π}{4}} (\sin (x) - \tan (x)) d x ?$

10.

$If \int_{a}^{b} x^{3} d x = 0 and \int_{a}^{b} x^{3} d x = \frac{2}{3}, then what are the values of a and b respectivley ?$