Mathematics

Find : $$\displaystyle\int {\dfrac{{{\text{si}}{{\text{n}}^{\text{2}}}{\text{x - co}}{{\text{s}}^{\text{2}}}{\text{x}}}}{{{\text{sin}}\;{\text{x}}\;{\text{cos}}\;{\text{x}}}}} \;{\text{dx}}$$


SOLUTION
$$I=\displaystyle\int \dfrac{\sin^2x-\cos^2x}{\sin x\cos x}dx$$

$$=\displaystyle\int \dfrac{\sin x}{\cos x}dx-\displaystyle\int \dfrac{\cos x}{\sin x}dx$$

$$=\log|\sec(x)|-\log|\sin x|+c$$

$$I=\log\dfrac{\sec x}{\sin x}+c$$.
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 86
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
$$\int { \sin ^{ 3 }{ \left( 2x+1 \right)  }  } dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Hard
Evaluate: $$\displaystyle \int e^{x} \dfrac {(2 + \sin 2x)}{\cos^{2}x} dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium
$$\int \dfrac{(x^2+1)a^x+\tan^{-1}x}{x^2+1}dx$$
  • A. $$\dfrac{a^x}{\log a}+\dfrac{(\tan^{-1}x)^3}{3}$$
  • B. $$\dfrac{a^2x}{\log a}+\dfrac{(\tan^{-1}x)^2}{2}$$
  • C. $$\dfrac{a^x}{\log a}+\dfrac{(\tan^{-1}x)}{2}$$
  • D. $$\dfrac{a^x}{\log a}+\dfrac{(\tan^{-1}x)^2}{2}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
$$\displaystyle \int 16x\sec ^2(2x^2+1) dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Easy
Evaluate:
$$ \int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer