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Popular >

integral of (12^x-5)

Solution

\int (1 2^{x} - 5) d x

Solution

\frac{1 2 ^{x}}{ln ( 12 )} - 5 x + C

Solution steps

\int 1 2^{x} - 5 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 1 2^{x} d x - \int 5 d x

\int 1 2^{x} d x = \frac{1 2 ^{x}}{ln ( 12 )}

\int 5 d x = 5 x

= \frac{1 2 ^{x}}{ln ( 12 )} - 5 x

Add a constant to the solution

= \frac{1 2 ^{x}}{ln ( 12 )} - 5 x + C

Graph

Popular Examples

integral of (2/(x^3)+3/(x^2)+3^x)

\int (\frac{2}{x ^{3}} + \frac{3}{x ^{2}} + 3^{x}) d x

integral of (6x^5)/((x^6-1)^2)

\int \frac{6 x ^{5}}{( x ^{6} - 1 ) ^{2}} d x

integral of x/((x-1)(x^2+x+1))

\int \frac{x}{( x - 1 ) ( x ^{2} + x + 1 )} d x

integral of (3-e^x)/(e^{7x)}

\int \frac{3 - e ^{x}}{e ^{7 x}} d x

integral of sqrt(1+2/x)

\int 1 + \frac{2}{x} d x

Frequently Asked Questions (FAQ)

What is the integral of (12^x-5) ?
The integral of (12^x-5) is (12^x)/(ln(12))-5x+C