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Popular >

integral of 6/x-8e^x

Solution

\int \frac{6}{x} - 8 e^{x} d x

Solution

6 ln ∣ x ∣ - 8 e^{x} + C

Solution steps

\int \frac{6}{x} - 8 e^{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 \frac{6}{x} d x - \int 8 e^{x} d x

\int \frac{6}{x} d x = 6 ln ∣ x ∣

\int 8 e^{x} d x = 8 e^{x}

= 6 ln ∣ x ∣ - 8 e^{x}

Add a constant to the solution

= 6 ln ∣ x ∣ - 8 e^{x} + C

Popular Examples

integral of (x-3)/(sqrt(9-(x-3)^2))

\int \frac{x - 3}{9 - ( x - 3 ) ^{2}} d x

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\frac{2 x}{1 + x ^{2}}

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

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

integral of ((sin(1/x)))/(x^2)

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

integral of ze^z+e^z

\int z e^{z} + e^{z} d z

Frequently Asked Questions (FAQ)

What is the integral of 6/x-8e^x ?
The integral of 6/x-8e^x is 6ln|x|-8e^x+C