∫ ((x-x3)(1/3)/x4) d x is equal to

Question

∫ ((x-x3)(1/3)/x4) d x is equal to (A) (3/8)((1/ x 2)-1)(4/3)+ C (B) (-3/8)((1/ x 2)+1)(4/3)+ C (C) (-3/8)((1/ x 2)-1)(4/3)+ C (D) (-3/4)(1-(1/ x 2))(4/3)+ C

Tardigrade Admin · Accepted Answer

∫ (((1/x2)-1)(1/3)/x3) d x Put (1/x2)-1=t ⇒ ∫ (- t (1/3)/2) dt =(-3 t (4/3)/8)+ C ⇒ (-3/8)((1/ x 2)-1)(4/3)+ C

Q. $\int \frac{( x - x ^{3} ) ^{\frac{1}{3}}}{x ^{4}} d x$ is equal to

$\frac{3}{8} (\frac{1}{x ^{2}} - 1)^{\frac{4}{3}} + C$

$\frac{- 3}{8} (\frac{1}{x ^{2}} + 1)^{\frac{4}{3}} + C$

$\frac{- 3}{8} (\frac{1}{x ^{2}} - 1)^{\frac{4}{3}} + C$

$\frac{- 3}{4} (1 - \frac{1}{x ^{2}})^{\frac{4}{3}} + C$

$\int \frac{( \frac{1}{x ^{2}} - 1 ) ^{\frac{1}{3}}}{x ^{3}} d x$
Put $\frac{1}{x ^{2}} - 1 = t$
$\Rightarrow \int \frac{- t ^{\frac{1}{3}}}{2} d t = \frac{- 3 t ^{\frac{4}{3}}}{8} + C$
$\Rightarrow \frac{- 3}{8} (\frac{1}{x ^{2}} - 1)^{\frac{4}{3}} + C$

Q. ∫x4(x−x3)31​​dx is equal to

83​(x21​−1)34​+C

8−3​(x21​+1)34​+C

8−3​(x21​−1)34​+C

4−3​(1−x21​)34​+C