Mathematics

# Integrate the following function with respect to $x$$\dfrac{4x-6}{(x^{2}-3x+5)^{3/2}}$

##### SOLUTION
Let,
$x^2-3x+5=t$

$\implies (2x-3)dx=dt$

Substituting these values, we get

$\int\dfrac{2dt}{t^{3/2}}$

$\implies \dfrac{-2\times2}{t^{1/2}}+C$

$\implies \dfrac{-4}{(x^2-3x+5)^{1/2}}+C$

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Medium
Evaluate $\displaystyle\int_{-1}^{1}5x^{4}\sqrt{x^{5}+1}\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
Evaluate: $\displaystyle \int \dfrac{(x-1)e^x}{(x+1)^3}dx=$
• A. $\dfrac{e^x}{x+1}$
• B. $\dfrac{e^x}{(x+1)^3}$
• C. $\dfrac{x\cdot e^x}{(x+1)}$
• D. $\dfrac{e^x}{(x+1)^2}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate $\int_{0}^{2} \dfrac{d x}{\left(17+8 x-4 x^{2}\right)\left[e^{6(1-x)}+1\right]}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integral:
$\displaystyle\int^1_0\dfrac{dx}{(2x-3)}$.

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\int { \cfrac { 2dx }{ { x }^{ 2 }-1 } }$ equals:
• A. $\cfrac { 1 }{ 2 } \log { \left( \cfrac { x-1 }{ x+1 } \right) } +C$
• B. $\log { \left( \cfrac { x+1 }{ x-1 } \right) } +C$
• C. $\log { \left( \cfrac { x-1 }{ x+1 } \right) } +C$
• D. $\cfrac { 1 }{ 2 } \log { \left( \cfrac { x+1 }{ x-1 } \right) } +C$