SHOW ALL YOUR WORK TO GET THE POINT. HINT, COMPLETE THE SQUARE IN LETTER \"D\" F

Question

SHOW ALL YOUR WORK TO GET THE POINT. HINT, COMPLETE THE SQUARE IN LETTER "D" FOR THE FIRST PART. THANKS

Explanation / Answer

1) a) int [ tanx 2^secx /cosx ]dx = int [ secx tanx 2^secx ]dx let secx = y secx tanx dx = dy = int [ 2^y ] dy = 2^y /ln(2) + C = 2^(secx) /ln(2) + C b) let e^x^2 = z 2x e^x^2 dx = dz ==> dz/2 = xe^x^2 int [ xe^x^2 * sec(e^x^2) ]dx + int [xe^x^2 tan(e^x^2) ] dx = int [secz]dz/2 + int [ tanz ]dz/2 = ln|secz + tanz| - ln|cosz| + C = ln|sec(e^x^2) + tan(e^x^2)| - ln|cos(e^x^2)| + C d) int [ 4/sqrt(-x^2+4x+1) ]dx + int [arcsin(x-2)/sqrt(1 - (x-2)^2) ]dx = int [ 4/sqrt(5-(x-2)^2 ]dx + int [arcsin(x-2)/sqrt(1 - (x-2)^2) ]dx = int [ (4/sqrt(5)) * 1/sqrt(1-((x-2)/sqrt5)^2 ]dx + int [arcsin(x-2)/sqrt(1 - (x-2)^2) ]dx = (4/sqrt(5)) * arcsin((x-2)/sqrt(5)) + [ [arcsin(x-2)]^2 ]/2 + C e) int [ (4x^5 - 9x^3 - 7x - 1)/(4x^2+3) ]dx = int [ (4x^5 + 3x^3 - 4x^3 - 3x - 4x^3 - 3x -4x^3-3x + 2x- 1) /(4x^2 + 3) ]dx = int [ (x^3(4x^2 + 3) - 3x(4x^2 + 3) +2x - 1) /(4x^2 + 3) ]dx = int [ x^3 - 3x + (2x-1)/(4x^2 + 3) ]dx = int [ x^3 - 3x + (1/4)*(8x-4)/(4x^2 + 3) ]dx = x^4/4 - 3x^2/2 + (1/4) * ln(4x^2+3) - (1/3) * arctan(2x/sqrt(3)) + C

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.