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Popular >

integral of x^45^x

Solution

\int x^{4} 5^{x} d x

Solution

\frac{5 ^{x} x ^{4}}{ln ( 5 )} - \frac{4}{ln ( 5 )} (\frac{5 ^{x} x ^{3}}{ln ( 5 )} - \frac{3}{ln ( 5 )} (\frac{5 ^{x} x ^{2}}{ln ( 5 )} - \frac{2}{ln ( 5 )} (\frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )}))) + C

Solution steps

\int x^{4} \cdot 5^{x} d x

Apply Integration By Parts

: \frac{5 ^{x} x ^{4}}{ln ( 5 )} - \int \frac{4 \cdot 5 ^{x} x ^{3}}{ln ( 5 )} d x

= \frac{5 ^{x} x ^{4}}{ln ( 5 )} - \int \frac{4 \cdot 5 ^{x} x ^{3}}{ln ( 5 )} d x

\int \frac{4 \cdot 5 ^{x} x ^{3}}{ln ( 5 )} d x = \frac{4}{ln ( 5 )} (\frac{5 ^{x} x ^{3}}{ln ( 5 )} - \frac{3}{ln ( 5 )} (\frac{5 ^{x} x ^{2}}{ln ( 5 )} - \frac{2}{ln ( 5 )} (\frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )})))

= \frac{5 ^{x} x ^{4}}{ln ( 5 )} - \frac{4}{ln ( 5 )} (\frac{5 ^{x} x ^{3}}{ln ( 5 )} - \frac{3}{ln ( 5 )} (\frac{5 ^{x} x ^{2}}{ln ( 5 )} - \frac{2}{ln ( 5 )} (\frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )})))

Add a constant to the solution

= \frac{5 ^{x} x ^{4}}{ln ( 5 )} - \frac{4}{ln ( 5 )} (\frac{5 ^{x} x ^{3}}{ln ( 5 )} - \frac{3}{ln ( 5 )} (\frac{5 ^{x} x ^{2}}{ln ( 5 )} - \frac{2}{ln ( 5 )} (\frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )}))) + C

Popular Examples

tangent of f(x)=(x^2-48)^4,\at x=7 tangent of

f (x) = (x^{2} - 48)^{4}, at x = 7

derivative of x/(3x+4ln(x))

\frac{d}{d x} (\frac{x}{3 x + 4 ln ( x )})

derivative of x+11

\frac{d}{d x} (x + 11)

integral from 0 to 3/2 of xcos(pi)x

\int_{0}^{\frac{3}{2}} x cos (π) x d x

integral of sqrt(1+v^2)

\int 1 + v^{2} d v

Frequently Asked Questions (FAQ)

What is the integral of x^45^x ?
The integral of x^45^x is