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Popular Calculus >

integral of 8e^{5x+e^{5x}}

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Solution

∫8e5x+e5xdx

Solution

58​ee5x+C
Solution steps
∫8e5x+e5xdx
Take the constant out: ∫a⋅f(x)dx=a⋅∫f(x)dx=8⋅∫e5x+e5xdx
Apply u-substitution
=8⋅∫eu+eu51​du
Take the constant out: ∫a⋅f(x)dx=a⋅∫f(x)dx=8⋅51​⋅∫eu+eudu
Apply u-substitution
=8⋅51​⋅∫evdv
Use the common integral: ∫evdv=ev=8⋅51​ev
Substitute back
=8⋅51​ee5x
Simplify 8⋅51​ee5x:58​ee5x
=58​ee5x
Add a constant to the solution=58​ee5x+C

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Frequently Asked Questions (FAQ)

  • What is the integral of 8e^{5x+e^{5x}} ?

    The integral of 8e^{5x+e^{5x}} is 8/5 e^{e^{5x}}+C
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