Mathematics

# $\int_0^{\pi /2} {\dfrac{1}{{1 + {{\tan }^3}x}}} dx$

##### SOLUTION
We have,
$I=\int _{ 0 }^{ \pi /2 }{ \dfrac { 1 }{ { 1+{ { \tan }^{ 3 } }x } } } dx........\left( 1 \right) \\$

Apply property, we get
$I=\int _{ 0 }^{ \pi /2 }{ \dfrac { 1 }{ { 1+{ { \cot }^{ 3 } }x } } } dx \\ I=\int _{ 0 }^{ \pi /2 }{ \dfrac { { { { \tan }^{ 3 } }x } }{ { { { \tan }^{ 3 } }x+1 } } } dx.........\left( 2 \right)$

On adding equation (1) and (2), we get
$\\ 2I=\int _{ 0 }^{ \pi /2 }{ dx } \\ I=\dfrac { \pi }{ 2 } \\ I=\dfrac { \pi }{ 4 }$

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

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