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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus

Integrate : $\int \large\frac{7}{9} x^{3/2} \tan ^5 (x^{5/2}) \sec^2 (x^{5/2}).dx$

$(a)\;\frac{7}{135}[\cot ^6(x^{5/2})]+c \qquad(b)\;\frac{7}{135}[\tan ^6(x^{5/2})]+c \qquad(c)\;\sin^6 (x^{5/2}) \qquad (d)\;None$

1 Answer

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$\int \large\frac{7}{9} x^{3/2} \tan ^5 (x^{5/2}) \sec^2 (x^{5/2}).dx$
=> $ \large\frac{7}{9} $$ \int x^{3/2} \tan ^5 (x^{5/2}) \sec^2 (x^{5/2}).dx$
$\tan (x^{5/2}) =t$
differentiate with respect to x
$\sec^2 x^{5/2} \times \large\frac{5}{2} $$x^{3/2} .dx$$=dt$
$x^{3/2} \sec^2 x^{5/2} .dx$$=\large\frac{5}{2}dt$
=> $\int \large\frac{7}{9} \times \frac{2}{5} $$t^5 dt$
=> $ \large\frac{14}{45} \bigg[ \frac{t^6}{6}\bigg]$$+c$
$\large\frac{7}{135}$$[\tan ^6(x^{5/2})]+c$
Hence b is the correct answer.
answered Dec 24, 2013 by meena.p