What is the integral of 1/(sqrt(x))-e^{5x}+ln(x) ?

The integral of 1/(sqrt(x))-e^{5x}+ln(x) is 2sqrt(x)-1/5 e^{5x}+xln(x)-x+C

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integral of 1/(sqrt(x))-e^{5x}+ln(x)

\int \frac{1}{x} - e^{5 x} + ln (x) d x

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

Solution steps

\int \frac{1}{x} - e^{5 x} + ln (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{1}{x} d x - \int e^{5 x} d x + \int ln (x) d x

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

\int e^{5 x} d x = \frac{1}{5} e^{5 x}

\int ln (x) d x = x ln (x) - x

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

Add a constant to the solution

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

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What is the integral of 1/(sqrt(x))-e^{5x}+ln(x) ?
The integral of 1/(sqrt(x))-e^{5x}+ln(x) is 2sqrt(x)-1/5 e^{5x}+xln(x)-x+C