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Popular >

integral of 1+ln(x)

Solution

\int 1 + ln (x) d x

Solution

x ln (x) + C

Solution steps

\int 1 + ln (x) d x

Apply Integration By Parts

: x (1 + ln (x)) - \int 1 d x

= x (1 + ln (x)) - \int 1 d x

\int 1 d x = x

= x (1 + ln (x)) - x

Simplify

x (1 + ln (x)) - x : x ln (x)

= x ln (x)

Add a constant to the solution

= x ln (x) + C

Popular Examples

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x \to 0 + lim (\frac{1}{x} \cdot sin (x^{2}))

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\int_{0}^{π} x \cdot sin (x) d x

sum from n=1 to infinity}3^{-2-2n of*2^{3n+1}

n = 1 \sum \infty 3^{- 2 - 2 n} \cdot 2^{3 n + 1}

(\partial)/(\partial x)(x/(2sqrt(2)))

\frac{\partial}{\partial x} (\frac{x}{2 2})

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

\int 3 - 2 x x^{2} d x

Frequently Asked Questions (FAQ)

What is the integral of 1+ln(x) ?
The integral of 1+ln(x) is xln(x)+C