Evaluate the integral.. x -1/ sqrt x dx at interval (1,9)
Evaluate the integral x(3sqrtx + 4sqrtx)
Evaluate the integral 1 + cosx/cosx r4om interval (0, pi/4)
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$\displaystyle \int{\frac{x - 1}{\sqrt{x}}\,dx} = \int{(x - 1)x^{-\frac{1}{2}}\,dx}$
$\displaystyle = \int{x^{\frac{1}{2}} - x^{-\frac{1}{2}}\,dx}$.
Now apply the power rule.
$\displaystyle \int{\frac{1 + \cos{x}}{\cos{x}}\,dx} = \int{(1 + \cos{x})\sec{x}\,dx}$
$\displaystyle = \int{\sec{x} + 1\,dx}$.
You should be able to go from here.
I assume for the other one, you mean
$\displaystyle \int{x(\sqrt[3]{x} + \sqrt[4]{x})\,dx} = \int{x(x^{\frac{1}{3}} + x^{\frac{1}{4}})\,dx}$
$\displaystyle = \int{x^{\frac{4}{3}} + x^{\frac{5}{4}}\,dx}$.
Now use the power rule.