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Popular >

integral of t^2et

Solution

\int t^{2} e t d t

Solution

\frac{e t ^{4}}{4} + C

Solution steps

\int t^{2} e t d t

Take the constant out:

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

= e \cdot \int t^{2} t d t

Simplify

t^{2} t : t^{3}

= e \cdot \int t^{3} d t

Apply the Power Rule

: \frac{t ^{4}}{4}

= e \frac{t ^{4}}{4}

Multiply fractions:

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

= \frac{e t ^{4}}{4}

Add a constant to the solution

= \frac{e t ^{4}}{4} + C

Popular Examples

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\int 6 sin^{3} (5 x) cos^{3} (5 x) d x

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\int 2 + 4 x + 42 x^{2} d x

integral of 2/((x+4)(x+6))

\int \frac{2}{( x + 4 ) ( x + 6 )} d x

integral of 3/(4x^2-1)

\int \frac{3}{4 x ^{2} - 1} d x

integral of 5/(xsqrt(4x^4-9))

\int \frac{5}{x 4 x ^{4} - 9} d x

Frequently Asked Questions (FAQ)

What is the integral of t^2et ?
The integral of t^2et is (et^4)/4+C