# Math Help - anti-derivative problems

1. ## anti-derivative problems

hi guys, i need help finding the anti-derivatives for these problems

Any help woud be appreciated

y' = tan(x)sec^2(x)

y' = 3x^(-1/2)

y' = -2cot^2(x)csc(x)

2. Originally Posted by sess
hi guys, i need help finding the anti-derivatives for these problems

Any help woud be appreciated

y' = tan(x)sec^2(x)
Make the substitution $z=\sec x$

y' = 3x^(-1/2)
Use the simple power rule...

--Chris

3. aight these are the answers that i got

y' = tan(x)sec^2(x) -> y = sec^2(x)tan(x)

y' = 3x^(-1/2) -> y = 1/(2x^(3/2))

y' = -2cot^2(x)csc(x) -> y = 2 (ln(abs(sin(x))))(csc(x))

did i get it?

4. pls help me out guys

5. Take the derivative of your answer and if it matches your integral than it is right.

The answer for the 1st is

$\frac{\sec^2{x}}{2} + c$

6. can u show me the steps on how u got that answer please?

7. Originally Posted by sess
can u show me the steps on how u got that answer please?
$\int \tan{x}\sec^2{x}~dx$

Like chris said

$\sec{x}= u$

$\sec{x}\tan{x}dx=du$

$\int u^{n}~du = \frac{u^{n+1}}{n+1} + C$

Can you finish up?

8. ok Ive no idea wat u just said

i do know that the first derivative of sec(x) is sec(x)tan(x) right?

i also know that the first derivative of tan(x) is sec^2(x)

Where do i go from here? I really must appologize to you 11rdc11
I have not understood the concept of finding the anti-derivative at all

Would you please be so kind and explain?

9. Originally Posted by sess
ok Ive no idea wat u just said

i do know that the first derivative of sec(x) is sec(x)tan(x) right?

i also know that the first derivative of tan(x) is sec^2(x)

Where do i go from here? I really must appologize to you 11rdc11
I have not understood the concept of finding the anti-derivative at all

Would you please be so kind and explain?
Ok do you know the basic integral formula

$\int u^{n}~du = \frac{u^{n+1}}{n+1} + C$

10. Originally Posted by 11rdc11
Ok do you know the basic integral formula

$\int u^{n}~du = \frac{u^{n+1}}{n+1} + C$
yep i understand that part

11. Originally Posted by sess
yep i understand that part
Ok n just represents the power.

So notice if we plug in the u of sub that I showed earlier the problem becomes the basic formula. Then just continue using the integral formula and back sub in the end.