Mathematics

# Evaluate: $\displaystyle \int \dfrac{1-cos x}{cos x (1+cos x)}dx$

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

#### Realted Questions

Q1 Subjective Hard
Prove that $\int \sin^{17}x dx = -\dfrac {\sin^{16}x \cos x}{17} + \dfrac {16}{17}\int \sin^{15}x dx + c$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate:
$\int { { x }^{ 2 }.{ e }^{ -2 } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle\int \dfrac{dx}{\sec^2x\tan^2x}=?$
• A. $\dfrac{3}{2}x+\tan x+\dfrac{\cos 2x}{4}+C$
• B. $\dfrac{3}{2}x+\tan x+\dfrac{\sin 2x}{4}+C$
• C. $\dfrac{2}{3}x-\tan x-\dfrac{\cos 2x}{4}+C$
• D. $-\left(\dfrac{3}{2}x+\cot x+\dfrac{\sin 2x}{4}\right)+C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Let $x > 0$ be a fixed real number. Then the integral $\int_{0}^{\infty} e^{-t} |x - t| dt$ is equal to.
• A. $x - 2e^{-x} + 1$
• B. $x + 2e^{-x} + 1$
• C. $-x - 2e^{-x} + 1$
• D. $x + 2e^{-x} - 1$

$\displaystyle\int x^n\log_ex\ dx$