Mathematics

# $\int sin^{5}x.cos^{100}x dx=$

$\frac{cos^{105}x}{105}+2\frac{cos^{103}x}{103}-\frac{cos^{101}x}{101}+c$

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

#### Realted Questions

Q1 Subjective Medium
Evaluate the following integral
$\int { \cfrac { a }{ b+c{ e }^{ x } } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate :
$\int {\dfrac{1}{{\left( {x + 2} \right)\left( {x + 2} \right)}}} dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate
$\displaystyle\int_{0}^{1}\dfrac{1-x^{2}}{(1+x^{2})^{2}}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
The value of $\displaystyle \int_{0}^{\dfrac {\pi}{4}} (\sqrt {\tan x} + \sqrt {\cot x})\,\, dx$ is equal to
• A. $\dfrac {\pi}{2}$
• B. $-\dfrac {\pi}{2}$
• C. $-\dfrac {\pi}{\sqrt {2}}$
• D. $\dfrac {\pi}{\sqrt {2}}$

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$