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Popular >

integral of 2x+ln(x)

Solution

\int 2 x + ln (x) d x

Solution

x^{2} + x ln (x) - x + C

Solution steps

\int 2 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 2 x d x + \int ln (x) d x

\int 2 x d x = x^{2}

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

= x^{2} + x ln (x) - x

Add a constant to the solution

= x^{2} + x ln (x) - x + C

Popular Examples

integral of (2x-7)/(x^2+9)

\int \frac{2 x - 7}{x ^{2} + 9} d x

integral of 1/2 (x+y)

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

integral of 1/(x^2+8x+21)

\int \frac{1}{x ^{2} + 8 x + 21} d x

integral of (sec(x)tan(x)-(csc(x))^2)

\int (sec (x) tan (x) - (csc (x))^{2}) d x

integral of 5/((x^2+1))

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

Frequently Asked Questions (FAQ)

What is the integral of 2x+ln(x) ?
The integral of 2x+ln(x) is x^2+xln(x)-x+C