Mathematics

Evaluate  $$\int\limits_0^1 {\dfrac{{2x}}{{5{x^2} + 1}}dx} $$


SOLUTION
$$\displaystyle \int_0^1\dfrac{2x}{5x^2+1}dx$$
$$x^2=t$$    $$2xdx=dt$$
$$\displaystyle \int_0^1\dfrac{dt}{st+1}$$
$$\left[\dfrac{1}{5}\log |5t+1|\right]^1_0$$
$$\left[\dfrac{1}{5}\log|5x^2+1|\right]^1_0$$
$$\dfrac{1}{5}\log 6$$
View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
Enroll Now For FREE

Realted Questions

Q1 Single Correct Hard
$$\displaystyle\int_{0}^{a}x^{4}\left ( a^{2}-x^{2} \right )^{1/2} dx$$ equals
  • A. $$\displaystyle\frac{\pi a^{5}}{32}$$
  • B. $$\displaystyle \frac{\pi a^{2}}{32}$$
  • C. None of these
  • D. $$\displaystyle\frac{\pi a^{6}}{32}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Evaluate : $$\displaystyle \int _{ 0 }^{ \log _{ e }{ 5 }  }{ \dfrac { { e }^{ x }\sqrt { { e }^{ x }-1 }  }{ { e }^{ x }+3 } dx }$$ 

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
Evaluate $$\displaystyle \int{\cos^{2}x\, dx}$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
Integrate the following function with respect to x
$$\displaystyle \int \left ( 5x^{2}+3x-2 \right )dx$$

  • A. $$\displaystyle \frac{5x^{3}}{3}-\frac{3x^{3}}{2}-2x+c$$
  • B. $$\displaystyle \frac{5x^{3}}{3}-\frac{3x^{2}}{2}+2x-c$$
  • C. $$\displaystyle \frac{5x^{3}}{3}+\frac{3x^{3}}{2}+2x+c$$
  • D. $$\displaystyle \frac{5x^{3}}{3}+\frac{3x^{2}}{2}-2x+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
Solve $$\int {{{\left( {2x + 3} \right)}^2}dx} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer