How do you integrate #int (sinx)(5^x)# using integration by parts?

Answer 1

I found:
#((-5^x)[cos(x)-ln(5)sin(x)])/(1+ln^2(5))#

Try this:

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

The user is interested in math and specifically in integration by parts.To integrate ( \int \sin(x) \cdot 5^x ) using integration by parts, let's use the formula:

[ \int u , dv = uv - \int v , du ]

Let's choose ( u = \sin(x) ) and ( dv = 5^x , dx ). Then, we have ( du = \cos(x) , dx ) and ( v = \frac{1}{\ln(5)} \cdot 5^x ).

Now, we can apply the integration by parts formula:

[ \begin{aligned} \int \sin(x) \cdot 5^x , dx & = -\frac{1}{\ln(5)} \cdot \sin(x) \cdot 5^x - \int -\frac{1}{\ln(5)} \cdot \cos(x) \cdot 5^x , dx \ & = -\frac{1}{\ln(5)} \cdot \sin(x) \cdot 5^x + \frac{1}{\ln(5)} \cdot \int \cos(x) \cdot 5^x , dx \end{aligned} ]

We can now integrate ( \int \cos(x) \cdot 5^x ) using integration by parts again or use a different method, such as recognizing that ( \int \cos(x) \cdot 5^x ) is of the form ( \int \cos(x) \cdot a^x ), which can be integrated using a simple substitution. Would you like to see that?

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7