Integrate 5 8 ln ⁡ ( 3 x 2 ) with respect to x.

Since&nbsp;58&nbsp;is constant with respect to&nbsp;x, move&nbsp;58&nbsp;out of the integral.58∫ln(3x2)dxIntegrate by parts using the formula&nbsp;∫udv=uv-∫vdu, where&nbsp;u=ln(3x2)&nbsp;and&nbsp;dv=1.58(ln(3x2)x-∫x(-2x)dx)Simplify.58(ln(3x2)x-∫-2dx)Apply the constant rule.58(ln(3x2)x-(-2x+C))Rewrite&nbsp;58(ln(3x2)x-(-2x+C))&nbsp;as&nbsp;58(ln(3x2)x+2x)+C.58(ln(3x2)x+2x)+C

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College
Calculus and Analysis
Integral Calculus
Integration by Parts

Spencer Lutz

Answered question

2022-05-13

Integrate

\frac{5}{8} ﻿ \ln (\frac{3}{x^{2}})

with respect to x.

Answer & Explanation

ele5ph1a7jl1

Beginner2022-05-14Added 21 answers

Since $\frac{5}{8}$ is constant with respect to $x$ , move $\frac{5}{8}$ out of the integral.

$\frac{5}{8} \int \ln (\frac{3}{x^{2}}) d x$

Integrate by parts using the formula $\int u d v = u v - \int v d u$ , where $u = \ln (\frac{3}{x^{2}})$ and $d v = 1$ .

$\frac{5}{8} (\ln (\frac{3}{x^{2}}) x - \int x (- \frac{2}{x}) d x)$

Simplify.

$\frac{5}{8} (\ln (\frac{3}{x^{2}}) x - \int - 2 d x)$

Apply the constant rule.

$\frac{5}{8} (\ln (\frac{3}{x^{2}}) x - (- 2 x + C))$

Rewrite $\frac{5}{8} (\ln (\frac{3}{x^{2}}) x - (- 2 x + C))$ as $\frac{5}{8} (\ln (\frac{3}{x^{2}}) x + 2 x) + C$ .

$\frac{5}{8} (\ln (\frac{3}{x^{2}}) x + 2 x) + C$

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