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x^(1/4) = tanu
(1/4)x^(-3/4) dx = (secu)^2 du
dx = 4 (tanu)^3. (secu)^2 du
∫dx/√(1+√x)
=∫4 (tanu)^3. (secu)^2 du/ secu
=4∫ (tanu)^3. (secu) du
=4∫ (tanu)^2 dsecu
=4∫ [(secu)^2-1] dsecu
=4[ (1/3)(secu)^3 - secu ] + C
= (4/3)(secu)^3 - 4secu + C
= (4/3)(1+√x)^(3/2) - 4√(1+√x) + C
(1/4)x^(-3/4) dx = (secu)^2 du
dx = 4 (tanu)^3. (secu)^2 du
∫dx/√(1+√x)
=∫4 (tanu)^3. (secu)^2 du/ secu
=4∫ (tanu)^3. (secu) du
=4∫ (tanu)^2 dsecu
=4∫ [(secu)^2-1] dsecu
=4[ (1/3)(secu)^3 - secu ] + C
= (4/3)(secu)^3 - 4secu + C
= (4/3)(1+√x)^(3/2) - 4√(1+√x) + C
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