Integrate

Asked by Topperlearning User | 30th Oct, 2016, 02:39: PM

Expert Answer:

integral 2 to the power of x square root of 4 to the power of x minus 1 end root d x
L e t space 2 to the power of x equals t rightwards double arrow space 2 to the power of x d x equals fraction numerator d t over denominator log 2 end fraction
t h e space i n t e g r a l space b e c o m e s
fraction numerator 1 over denominator log 2 end fraction integral square root of t squared minus 1 end root d t
equals fraction numerator 1 over denominator log 2 end fraction open parentheses t over 2 square root of t squared minus 1 end root minus 1 half log open parentheses t plus square root of t squared minus 1 end root close parentheses close parentheses plus c o n s tan t
equals fraction numerator 1 over denominator log 2 end fraction open parentheses 2 to the power of x over 2 square root of 4 to the power of x minus 1 end root minus 1 half log open parentheses 2 to the power of x plus square root of 4 to the power of x minus 1 end root close parentheses close parentheses plus c o n s tan t

Answered by  | 30th Oct, 2016, 04:39: PM