1. ## More integrals

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)

2. Originally Posted by Jgirl689
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)
$\int{x(3\sqrt{x} + 4\sqrt{x})\,dx} = \int{7x^{\frac{3}{2}}\,dx}$

$= \frac{14}{5}x^{\frac{5}{2}} + C$

$= \frac{14\sqrt{x^5}}{5} + C$.

With the rest, you'll need to put brackets where they're needed. They're too hard to read.

3. Originally Posted by Jgirl689
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)
1. (x-1)/(sqrt x) from interval (1,9)
2. (1+cosx)/(cosx) from interval (0, pie/4)
By the way, the other one posted is supposed to be (sqrt x ^3 + sqrt x ^4)..3 and 4 are roots..

4. Originally Posted by Jgirl689
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)
To check answers (and perhaps even get solutions) use Wolfram|Alpha

5. Thanks but none of them show how the steps are done, some do even show for integrals ...someone please help me on these!

6. Originally Posted by Jgirl689
Thanks but none of them show how the steps are done, some do even show for integrals ...someone please help me on these!
For 1st and 3rd,

Use:

$\frac{a \pm b}{c}=\frac{a}{c} \pm \frac{b}{c}$ for $c \neq 0$.

7. Originally Posted by Jgirl689
1. (x-1)/(sqrt x) from interval (1,9)
2. (1+cosx)/(cosx) from interval (0, pie/4)
By the way, the other one posted is supposed to be (sqrt x ^3 + sqrt x ^4)..3 and 4 are roots..
$\int{\frac{x - 1}{\sqrt{x}}\,dx} = \int{(x - 1)x^{-\frac{1}{2}}\,dx}$

$= \int{x^{\frac{1}{2}} - x^{-\frac{1}{2}}\,dx}$.

Now apply the power rule.

$\int{\frac{1 + \cos{x}}{\cos{x}}\,dx} = \int{(1 + \cos{x})\sec{x}\,dx}$

$= \int{\sec{x} + 1\,dx}$.

You should be able to go from here.

I assume for the other one, you mean

$\int{x(\sqrt[3]{x} + \sqrt[4]{x})\,dx} = \int{x(x^{\frac{1}{3}} + x^{\frac{1}{4}})\,dx}$

$= \int{x^{\frac{4}{3}} + x^{\frac{5}{4}}\,dx}$.

Now use the power rule.