General Logarithmic & Exponential Functions?

Question

∫ 2^5x+1 dx

I have my u=5x+1

Answer 1

ʃ2^{5x + 1} dx

let u = 5x + 1

Apply derivative to each side

du = 5dx

Substitute dx   =(1 / 5) du

(1 / 5) ʃ 2^u du = (1 / 5 ) 2^u / log2 + C

                       =2^u / 5log2 + c

Substitute u = 5x + 1

                       = 2^{5x + 1} / 5log2 + C

                       =2^{5x + 1} / log2⁵ + C.