What is the integral from 1 to 3 of ((ax)^3+e^{-bx}) ?

The integral from 1 to 3 of ((ax)^3+e^{-bx}) is a^3*20-(e^{-3b}-e^{-b})/b

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integral from 1 to 3 of ((ax)^3+e^{-bx})

\int_{1}^{3} ((a x)^{3} + e^{- b x}) d x

a^{3} \cdot 20 - \frac{e ^{- 3 b} - e ^{- b}}{b}

Solution steps

\int_{1}^{3} (a x)^{3} + e^{- b x} d x

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= \int_{1}^{3} a^{3} x^{3} + e^{- b x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{3} a^{3} x^{3} d x + \int_{1}^{3} e^{- b x} d x

\int_{1}^{3} a^{3} x^{3} d x = a^{3} \cdot 20

\int_{1}^{3} e^{- b x} d x = - \frac{e ^{- 3 b} - e ^{- b}}{b}

= a^{3} \cdot 20 - \frac{e ^{- 3 b} - e ^{- b}}{b}

\int_{0}^{2} 4 x d x

x \to 1 lim (1 - x)

y^{^{''}} + 16 y = csc^{2} (4 t)

\int_{1}^{9} \frac{2}{x ^{3}} d x

What is the integral from 1 to 3 of ((ax)^3+e^{-bx}) ?
The integral from 1 to 3 of ((ax)^3+e^{-bx}) is a^3*20-(e^{-3b}-e^{-b})/b