Question

I = \int e^{5x} \sin^3(e^{5x}) \cos^6(e^{5x}) dx we make the substitution t = e^{5x} to obtain I = \int f(t)dt where f(t) = Then we make the substitution u = \cos(t) and obtain I = \int g(u)du where g(u) = Now you can calculate the value of the integral (in terms of x) which is I = +C where C is an arbitrary constant.

          I = \int e^{5x} \sin^3(e^{5x}) \cos^6(e^{5x}) dx
we make the substitution t = e^{5x} to obtain I = \int f(t)dt where
f(t) = 
Then we make the substitution u = \cos(t) and obtain I = \int g(u)du where
g(u) = 
Now you can calculate the value of the integral (in terms of x) which is
I = 
+C
where C is an arbitrary constant.

I = ∫e^5x sin^3(e^5x) cos^6(e^5x) dx
we make the substitution t = e^5x to obtain I = ∫f(t)dt where
f(t) =
Then we make the substitution u = cos(t) and obtain I = ∫g(u)du where
g(u) =
Now you can calculate the value of the integral (in terms of x) which is
I =
+C
where C is an arbitrary constant.

Added by Hannah S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/06/2023

Step 1

Step 1: Make the substitution t = e^(5x) to rewrite the integral as I = ∫ f(t)dt, where f(t) = sin^3(t)cos^6(t). Show more…

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I = ∫ e^(5x)sin^3(e^(5x))cos^6(e^(5x))dx We make the substitution t = e^(5x) to obtain I = ∫ f(t)dt where f(t) = Then we make the substitution u = cos(t) and obtain I = ∫ g(u)du where g(u) = Now you can calculate the value of the integral (in terms of x) which is = I + C where C is an arbitrary constant.