What is the integral of (10^{6x}+1)/(10^{3x)} ?

The integral of (10^{6x}+1)/(10^{3x)} is (1000^x)/(3ln(10))-1/(3ln(10)*1000^x)+C

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integral of (10^{6x}+1)/(10^{3x)}

\int \frac{1 0 ^{6 x} + 1}{1 0 ^{3 x}} d x

\frac{100 0 ^{x}}{3 ln ( 10 )} - \frac{1}{3 ln ( 10 ) \cdot 100 0 ^{x}} + C

Solution steps

\int \frac{1 0 ^{6 x} + 1}{1 0 ^{3 x}} d x

Expand

\frac{1 0 ^{6 x} + 1}{1 0 ^{3 x}} : 100 0^{x} + \frac{1}{100 0 ^{x}}

= \int 100 0^{x} + \frac{1}{100 0 ^{x}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 100 0^{x} d x + \int \frac{1}{100 0 ^{x}} d x

\int 100 0^{x} d x = \frac{100 0 ^{x}}{3 ln ( 10 )}

\int \frac{1}{100 0 ^{x}} d x = - \frac{1}{3 ln ( 10 ) \cdot 100 0 ^{x}}

= \frac{100 0 ^{x}}{3 ln ( 10 )} - \frac{1}{3 ln ( 10 ) \cdot 100 0 ^{x}}

Add a constant to the solution

= \frac{100 0 ^{x}}{3 ln ( 10 )} - \frac{1}{3 ln ( 10 ) \cdot 100 0 ^{x}} + C

What is the integral of (10^{6x}+1)/(10^{3x)} ?
The integral of (10^{6x}+1)/(10^{3x)} is (1000^x)/(3ln(10))-1/(3ln(10)*1000^x)+C