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$\int \frac{t^{4} d t}{1 - t^{10}} i s$

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110log1−t51+t5+c

15log1+t51−t5+c

−110log1−t51+t5+c

110log1+t51−t5+c

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detailed solution

Correct option is D

∫t4dt1−t10dt=∫t4dt1−(t5)2t5=u⇒5t4dt=du Use ∫1a2−x2dx=12alog⁡a+xa−x+c=15∫du12−u2=15⋅12(1)log⁡1+u1−u+c=110log1+t51−t5+c

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∫t4dt1−t10is

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$\int \frac{t^{4} d t}{1 - t^{10}} i s$