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Popular Calculus >

integral of xt

Solution

\int x t d t

Solution

\frac{x t ^{2}}{2} + C

Solution steps

\int x t d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= x \cdot \int t d t

Apply the Power Rule

= x \frac{t ^{2}}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x t ^{2}}{2}

Add a constant to the solution

= \frac{x t ^{2}}{2} + C

Graph

Popular Examples

integral of (sin(1/u))/(u^3)

\int \frac{sin ( \frac{1}{u} )}{u ^{3}} d u

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

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

integral of e^{2x}e^{e^x}

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

integral of arctan(1/t)

\int arctan (\frac{1}{t}) d t

integral of (3x+2)/(sqrt(x^2-4x+20))

\int \frac{3 x + 2}{x ^{2} - 4 x + 20} d x

Frequently Asked Questions (FAQ)

What is the integral of xt ?
The integral of xt is (xt^2)/2+C