What is the integral of e^x-ln(x) ?

The integral of e^x-ln(x) is e^x-xln(x)+x+C

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integral of e^x-ln(x)

\int e^{x} - ln (x) d x

e^{x} - x ln (x) + x + C

Solution steps

\int e^{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 e^{x} d x - \int ln (x) d x

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

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

= e^{x} - (x ln (x) - x)

Simplify

= e^{x} - x ln (x) + x

Add a constant to the solution

= e^{x} - x ln (x) + x + C

\int \frac{x ^{2}}{4 + x ^{6}} d x

x^{^{''}} + 3 x = 0

\frac{\partial}{\partial x} (x^{2} e^{- y})

\int 2 cos (x) - \frac{3}{1 - x ^{2}} d x

f (x) = 2 x^{2}, at x = 3