Mathematics

# Integrate $\displaystyle \int \cos^3x \ dx$

##### SOLUTION
Consider $I=\displaystyle \int \cos^3 x \ dx$

$I=\displaystyle \int \dfrac{\cos 3x+3\cos x}{4} \ dx$      $[\because cos3A=\left( 4\cos ^{ 3 }{ A } -3\cos { A }\right)]$

$I=\displaystyle \dfrac{1}{4}\int \cos 3x +3\cos x \ dx$

$I=\displaystyle \dfrac{1}{4}\int \cos 3x\ dx +\dfrac{1}{4} \int 3\cos x \ dx$

$I=\displaystyle \dfrac{1}{4}\left[\dfrac{\sin 3x}{3}+3\sin x\right]+C$

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

#### Realted Questions

Q1 Subjective Medium
Evaluate $\displaystyle\int_{0}^{\pi/4}\dfrac{\tan^{3}x}{1+\cos 2x}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
If $f(x)=\left| \begin{matrix} x & \cos { x } & { e }^{ { x }^{ 2 } } \\ \sin { x } & { x }^{ 2 } & \sec { x } \\ \tan { x } & 1 & 2 \end{matrix} \right|$ then the value of $\displaystyle \int _{-\pi/2}^{\pi/2}f(x)dx$ is equal to
• A. $1$
• B. $2$
• C. $none\ of\ these$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Integrate following with respect to $x$.
(i) $\sqrt{x^2 + 4}$          (ii) $\sqrt{x^2 + 2x + 5}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Solve $\displaystyle\int \dfrac{dt}{t\sqrt{t^{2}-1}}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
The value of $\displaystyle\int\limits_{1}^{e^2}\dfrac{dx}{x}$
• A. $1$
• B. $-1$
• C. $-2$
• D. $2$