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Popular >

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

= 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

Popular Examples

integral of (3x^2+5x-6)

\int (3 x^{2} + 5 x - 6) d x

integral of 1/(sqrt(y)-y)

\int \frac{1}{y - y} d y

integral of tan^2(θ-1)

\int tan^{2} (θ - 1) d θ

integral of (1/(x^2)+1/(x^3))

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

integral of sec^4(2x)tan^2(2x)

\int sec^{4} (2 x) tan^{2} (2 x) 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