Mathematics

Solve :
$$\displaystyle\int { \tan ^{ 2 }{ \left( 2x-3 \right)  }  } dx$$


SOLUTION
$$\displaystyle\int{{\tan}^{2}{\left(2x-3\right)}dx}$$

Let $$t=2x-3\Rightarrow\,dt=2\,dx$$

$$=\dfrac{1}{2}\displaystyle\int{{\tan}^{2}{t}\ dt}$$

$$=\dfrac{1}{2}\displaystyle\int{\left({\sec}^{2}{t}-1\right)dt}$$

$$=\dfrac{1}{2}\left[\tan{t}-t\right]+c$$ where $$\displaystyle\int{{\sec}^{2}{x}dx}=\tan{x}+c$$ and $$\displaystyle\int{dx}=x+c$$

$$=\dfrac{1}{2}\left[\tan{\left(2x-3\right)}-2x-3\right]+c$$ where $$t=2x-3$$

$$=\dfrac{1}{2}\tan{\left(2x-3\right)}-x-\dfrac{3}{2}+c$$

$$=\dfrac{1}{2}\tan{\left(2x-3\right)}-x+C$$ where $$-\dfrac{3}{2}+c=C$$
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 84
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
Integrate $$\int {({{\sin }^{ - 1}}} x{)^2}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Hard
Prove that:
$$\displaystyle \int_{0}^{\dfrac {\pi}{2}}(2\log \sin x-\log \sin 2x)dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Hard
 If $$\displaystyle I = \int _{0}^{1} \frac{dx}{(1+ x)(2 + x)\sqrt{x(1-x)}}$$ then $$I$$ equals
  • A. $$ 2\pi $$
  • B. $$\pi$$
  • C. $$\displaystyle \frac{\pi}{2} $$
  • D. $$\displaystyle \frac{\pi}{\sqrt{6}}(\sqrt{3}-1)$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
Solve$$\displaystyle \int^{\pi/2} _0 \dfrac{x \ sin x \ cos x}{cos^4 x + sin^4 x} dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
Evaluate $$\int { \dfrac { { x }^{ 2 } }{ \sqrt { { x }^{ 6 }+{ a }^{ 6 } }  } dx }$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer