Evaluate the following integrals. ∫x10xdx

eozoischgc

eozoischgc

Answered

2021-12-27

Evaluate the following integrals.
x10xdx

Answer & Explanation

Jillian Edgerton

Jillian Edgerton

Expert

2021-12-28Added 34 answers

Step 1
Given: I=x(10)xdx
for evaluating given integral, we will use integral by parts theorem
according to this theorem
f(x)g(x)dx=g(x)f(x)dx[(g(x))f(x)dx]dx+c
Step 2
so,
I=(x)(10x)dx
=x(10x)dx[110xdx]dx
(axdx=axlna+c)
=x(10xln10)(10xln10)dx+c
=x(10x)ln101ln10(10xln10)+c
hence, given integral is x(10x)ln1010x(ln10)2+c.
Andrew Reyes

Andrew Reyes

Expert

2021-12-29Added 24 answers

x10xdx
Integration piece by piece: fg=fgfg
f=x,g=10x
=x10xln(10)10xln(10)dx
10xln(10)dx
Let's apply linearity:
=1ln(10)10xdx
10xdx
Integral of exponential function:
axdx=axln(a) at a=10:
=10xln(10)
1ln(10)10xdx
=10xln2(10)
x10xln(10)10xln(10)dx
=x10xln(10)10xln2(10)
x10xdx
=x10xln(10)10xln2(10)+C
Let's rewrite / simplify:
=(ln(10)x1)10xln2(10)+C
Vasquez

Vasquez

Expert

2022-01-07Added 457 answers

x×10xdx
Prepare for integration by parts
u=x
dv=10xdx
du=dx
v=10xln(10)
x×10xln(10)10xln(10)dx
x×10xln(10)1ln(10)×10xdx
x×10xln(10)1ln(10)×10xln(10)
Simplify
x×10xln(10)10xln(10)2
Add C
Answer:
x×10xln(10)10xln(10)2+C

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?