If 2^x 1-4^x d x=k ⁻¹ (2^x )+C , then k is equal to

Step-by-step solution

Let I= 2^x 1-4^x d x Let 2^x=t aligned & 2^x 2 d x=d t & I= 1 2 1 1-t^2 d t & = 1 2 ⁻¹(t)+C & = 1 2 ⁻¹ (2^x )+C aligned But I=k ⁻¹ (2^x )+C , k= 1 2