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Popular Calculus >

integral of x*x'

Solution

\int x \cdot x^{'} d x

Solution

x^{2} x' - \frac{x ^{2}}{2} + C

Solution steps

\int x x^{'} d x

Apply Integration By Parts

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

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

= x^{2} x^{^{'}} - \frac{x ^{2}}{2}

Add a constant to the solution

= x^{2} x^{^{'}} - \frac{x ^{2}}{2} + C

Graph

Popular Examples

integral of 1/(xsqrt(5+ln(3x)))

\int \frac{1}{x 5 + ln ( 3 x )} d x

integral of 3x-9

\int 3 x - 9 d x

integral of (4w^2-12w+3w^5-17)/(-2+w^2)

\int \frac{4 w ^{2} - 12 w + 3 w ^{5} - 17}{- 2 + w ^{2}} d w

integral of (x+5)(x-4)

\int (x + 5) (x - 4) d x

integral of cos(x^3)3x^2

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

Frequently Asked Questions (FAQ)

What is the integral of x*x' ?
The integral of x*x' is x^2x'-(x^2)/2+C