{(1- x)²/7}}{(1+ x)^{9/7}} dx =

Correct Answer is : 711(tan⁡x2)11/7+C7/11≤ft(/2)¹1/7}+C117(tan2x)11/7+C

Correct Answer is : 711(tan⁡x2)11/7+C7/11≤ft(/2)¹1/7}+C117(tan2x)11/7+C

Test Index

TS EAMCET 4-Aug-2021 Shift 1 Question Paper

Section: Mathematics

Question : 77 of 160

Marks: +1, -0

\int \frac{(1-\cos x)^{2/7}}{(1+\cos x)^{9/7}}

dx

Solution: 👈: Video Solution

\int\;\frac{(1-\cos x)^{2/7}}{(1+\cos x)^{9/7}} d x

=\int\;\frac{(1-\cos x)^{2/7}}{(1+\cos x)(1+\cos x)^{2/7}} d x

=\int\left(\;\frac{1-\cos x}{1+\cos x}\right)^{2/7}\;\frac{d x}{1+\cos x}

=\int\left(\;\frac{2 \sin^{2} \frac{x}{2}}{2 \cos^{2} \frac{x}{2}}\right)^{2/7} \cdot \;\frac{d x}{2 \cos^{2} \frac{x}{2}}

=\int\left(\tan^{2} \frac{x}{2}\right)^{2/7} \cdot \;\frac{1}{2} \sec^{2} \frac{x}{2} d x

=\;\frac{1}{2} \int \tan^{4/7} \frac{x}{2} \cdot \sec^{2} \frac{x}{2} d x

Let

\tan \frac{x}{2}=t

\Rightarrow \;\; \sec^{2} \frac{x}{2} d x \;\; =2 d t

\;\; =\int t^{4/7} d t

\;\; =\frac{t^{\frac{4}{7}+1}}{\frac{4}{7}+1}+C=\frac{7}{11} t^{11/7}+C

\;\; =\frac{7}{11} \tan^{11/7} \frac{x}{2}+C

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