Saturday

December 20, 2014

December 20, 2014

Posted by **Candice** on Thursday, April 19, 2012 at 6:26am.

the integral from 0 to 4 of

(x+1)/(16+x^2) dx

the answers are log(sqrt2) + pi/16

Could you please take me through how to get to that answer please, thank you very much!

- Math -
**Reiny**, Thursday, April 19, 2012 at 8:14amsplit (x+1)/(16+x^2) into x/(16+x^2) + 1/(16+x^2)

the integral of x/(16+x^2) =**(1/2) ln(16+x^2)**

( I recognized the ln derivative pattern)

for the integral of 1/(16+x^2) I went to my "archaic" integral talbles and go**(1/4) tan^-1 (x/4)**

so the integral would be**(1/2)ln(16+x^2) + (1/4)tan^-1 (x/4)**

so from 0 to 4 would give me

( (1/2)ln(32) + (1/4)tan^-1 (1) - ( (1/2) ln16 + (1/4)tan^-1 (0) )

= ln √32 + (1/4)(π/4) - ln √16 - (1/4)(0)

= ln (4√2) + π/16 - ln 4 - 0

= ln4 + ln √2 + π/16 - ln4

= ln √2 + π/16

**Answer this Question**

**Related Questions**

Calc Help Please - Evaluate the integral. integral 1/((x-2)(x+2)) Note: Use an ...

Precalculus - Given: f(x) = X^2-x evaluate: f(sqrt2 + 3) I have worked out this ...

Algebra II - Please check answers: Use the equation of the exponential function ...

Math - complex numbers - These questions are related to de moivre's theorem: z^n...

math - find d/dx of the integral from 1 to 2x of the (sqrt t^2+1)dt at x=sqrt2 ...

Trigonometry (Help and Check) - Evaluate (exact answers): a) sin^-1(cos30) Need ...

math - express the limit as a definite integral. Do Not Evaluate the integral. ...

Precalculus - PLEASE HELP ME WITH THESE QUESTION AS MUCH AS POSSIBLE!! Evaluate...

Math - 1) evaluate: integral of (3x^2 + 5x - 1 + 3/x) dx x^3/3 + x^2/5 - x Is ...

Math - The problem 8^x = 16^x+2 the choices a)8 and b)-8. Help please! Given ...