-x-3-1-x-2-1-3dx is equal to20-3-1-x-2-2-3-2x-2-3-C3-20-1-x-2-2-3-2x-2-3-CNone of these3-20-1-x-2-2-3-2x-2-3-C

The correct option is D 3/20(1+x^2)^2/3(2x^2 3)+CPut 1+x^2=t^3⇒ 2x dx=3t^2 dt ∴∫x^3/(1+x^2)^1/3dx = ∫x^2.x/(1+x^2)^1/3dx =3/2∫ (t^3 1)t dt = 3/2∫ (t^4 t)dt ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Integration by Substitution

∫x^3/(1+x^2)^...

Question

$\int \frac{x^{3}}{(1 + x^{2})^{1 / 3}} d x$ is equal to

\frac{20}{3} (1 + x^{2})^{\frac{2}{3}} (2 x^{2} - 3) + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{3}{20} (1 + x^{2})^{\frac{2}{3}} (2 x^{2} - 3) + C

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{3}{20} (1 + x^{2})^{\frac{2}{3}} (2 x^{2} + 3) + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{3}{20} (1 + x^{2})^{\frac{2}{3}} (2 x^{2} - 3) + C$
Put $1 + x^{2} = t^{3} \Rightarrow 2 x d x = 3 t^{2} d t ∴ \int \frac{x^{3}}{(1 + x^{2})^{1 / 3}} d x = \int \frac{x^{2} . x}{(1 + x^{2})^{1 / 3}} d x = \frac{3}{2} \int (t^{3} - 1) t d t = \frac{3}{2} \int (t^{4} - t) d t = \frac{3}{2} (\frac{t^{5}}{5} - \frac{t^{2}}{2}) + C = \frac{3}{20} t^{2} (2 t^{3} - 5) + C = \frac{3}{20} (1 + x^{2})^{\frac{2}{3}} (2 x^{2} - 3) + C$

Suggest Corrections

Similar questions

\int_{0}^{1} \frac{1 - x^{2}}{{(1 + x^{2})}^{2}} d x

\int \frac{x^{3}}{x + 1} d x

is equal to

(a) x + \frac{x^{2}}{2} + \frac{x^{3}}{3} - \log |1 - x| + C (b) x + \frac{x^{2}}{2} - \frac{x^{3}}{3} - \log |1 - x| + C (c) x - \frac{x^{2}}{2} - \frac{x^{3}}{3} - \log |1 + x| + C (d) x - \frac{x^{2}}{2} + \frac{x^{3}}{3} - \log |1 + x| + C

Q. If the length of a median of an equilateral triangle is x cm, then its area is

(a) x²

(b)

\frac{\sqrt{3}}{2} x^{2}

(c)

\frac{x^{2}}{\sqrt{3}}

(d)

\frac{x^{2}}{2}

Q. 3 root 3²x2^³

(1 + x)^{21} + (1 + x)^{22} + . . . + (1 + x)^{30}

coefficient of

x^{5}

Join BYJU'S Learning Program

∫x3(1+x2)1/3dx is equal to

The correct option is B 320(1+x2)23(2x2−3)+CPut 1+x2=t3⇒2x dx=3t2 dt∴∫x3(1+x2)1/3dx=∫x2.x(1+x2)1/3dx=32∫(t3−1)t dt=32∫(t4−t)dt=32(t55−t22)+C=320t2(2t3−5)+C=320(1+x2)23(2x2−3)+C

$\int \frac{x^{3}}{(1 + x^{2})^{1 / 3}} d x$ is equal to