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Popular >

integral of x^3e^3

Solution

\int x^{3} e^{3} d x

Solution

\frac{e ^{3} x ^{4}}{4} + C

Solution steps

\int x^{3} e^{3} d x

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{4}}{4}

= e^{3} \frac{x ^{4}}{4}

Multiply fractions:

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

= \frac{e ^{3} x ^{4}}{4}

Add a constant to the solution

= \frac{e ^{3} x ^{4}}{4} + C

Popular Examples

derivative of f(x)=x^2-sec(x)+1 derivative of

f (x) = x^{2} - sec (x) + 1

laplacetransform tcos(4t)laplace transform

t cos (4 t)

tangent of f(x)=x^3-3x^2-9x+5,\at x=-12 tangent of

f (x) = x^{3} - 3 x^{2} - 9 x + 5, at x = - 12

integral from 0 to 2 of 0

\int_{0}^{2} 0 d x

y^'=(0.5+sin(t))(y/5)

y^{^{'}} = (0.5 + sin (t)) (\frac{y}{5})

Frequently Asked Questions (FAQ)

What is the integral of x^3e^3 ?
The integral of x^3e^3 is (e^3x^4)/4+C