Hi! I need help solving letter e shown below. I already have the answer provided, which is ?2arctan(2x)+4x2+14x?+C. I feel like I am missing a step. Can you please solve this step by step so I can see where to go from here?

e. 8 dx Partial Fractions (4 x 2 + 1 ) 2 8 = AX + B CX + D (4x2 +1) 2 4 x2 + 1 (4 x2 + 1 ) 2 8 = (Ax + B) (4x3+1) + CX+D = 4Ax+Ax + 4BX2 +B+ CX+0 = 4AX3 + 4 Bx2 + (A+()x+ (B+D) 4A=0 4B=0 A+6=0 B+0:8 A=0 C=0 B= 8-D 4 ( 8 - D) = 0 B=0 32-40=-32 D = 8 8 dx ( 4 * 2 + 1) 2 CO dx (4 x2 +1 ) 2 X = tano x1+4 X= 2tano dx= seczo 4x2 +1 - (2+an0+1)2 4 tan20 + 1 x = tane 1 seczo do (2 tan 0 + 1) 2 sec20 do 4 tan?0+1 N seczo do tan 28 + 1 2 I . sec o as sec zo