∫ (3 e x +5 e - x /4 e x -5 e - x ) dx = Ax + B ln |4 e 2 x -5|+ C then

Question

∫ (3 e x +5 e - x /4 e x -5 e - x ) dx = Ax + B ln |4 e 2 x -5|+ C then (A) A =-1, B =-7 / 8 ; C = const. of integration (B) A =1, B =7 / 8 ; C = const. of integration (C) A =-1 / 8, B =7 / 8 ; C = const. of integration (D) A =-1, B =7 / 8 ; C = const. of integration

Tardigrade Admin · Accepted Answer

I=∫ (3 ex+5 e-x/4 ex-5 e-x) d x=∫ (3 e2 x+5/4 e2 x-5) d x Let 3 e 2 x +5= A (4 e 2 x -5)+ B (8 e 2 x ) ∴ 4 A+8 B=3 text and 5 A=5 ⇒ A=-1 and 5 A =5 ⇒ A =-1 ∴ B =(7/8) ∴ I = Ax + B ln (4 e 2 x -5)+ C text when A =-1 text and B =(7/8)

Q. $\int \frac{3 e ^{x} + 5 e ^{- x}}{4 e ^{x} - 5 e ^{- x}} d x = A x + B ln ∣ ∣ 4 e^{2 x} - 5 ∣ ∣ + C$ then

$A = - 1, B = - 7/8; C =$ const. of integration

$A = 1, B = 7/8; C =$ const. of integration

$A = - 1/8, B = 7/8; C =$ const. of integration

$A = - 1, B = 7/8; C =$ const. of integration

Q. ∫4ex−5e−x3ex+5e−x​dx=Ax+Bln∣∣​4e2x−5∣∣​+C then

A=−1,B=−7/8;C= const. of integration

A=1,B=7/8;C= const. of integration

A=−1/8,B=7/8;C= const. of integration

A=−1,B=7/8;C= const. of integration

I=∫4ex−5e−x3ex+5e−x​dx=∫4e2x−53e2x+5​dx Let 3e2x+5=A(4e2x−5)+B(8e2x) ∴4A+8B=3 and 5A=5⇒A=−1 and 5A=5⇒A=−1 ∴B=87​ ∴I=Ax+Bln(4e2x−5)+C when A=−1 and B=87​

Q. $\int \frac{3 e ^{x} + 5 e ^{- x}}{4 e ^{x} - 5 e ^{- x}} d x = A x + B ln ∣ ∣ 4 e^{2 x} - 5 ∣ ∣ + C$ then

$A = - 1, B = - 7/8; C =$ const. of integration

$A = 1, B = 7/8; C =$ const. of integration

$A = - 1/8, B = 7/8; C =$ const. of integration

$A = - 1, B = 7/8; C =$ const. of integration