∫x132+x122dx is equal to

∫x132+x122dx Let x=t6dx=6t5dt=∫t22+t326t5dt=6∫t74+t6+4t3dt=6∫4t7+4t10+t13dt=6∫4t88+4t1111+t1414+C=3x43+2411x116+37⋅x73+C

∫x132+x122dx is equal to

∫x132+x122dx Let x=t6dx=6t5dt=∫t22+t326t5dt=6∫t74+t6+4t3dt=6∫4t7+4t10+t13dt=6∫4t88+4t1111+t1414+C=3x43+2411x116+37⋅x73+C

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

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

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$3 x^{\frac{3}{4}} + \frac{24}{11} x^{\frac{11}{6}} + \frac{3}{7} x^{\frac{3}{7}} + c$

$3 x^{\frac{3}{4}} + \frac{24}{11} x^{\frac{11}{6}} + \frac{7}{3} x^{\frac{7}{3}} + c$

$3 x^{\frac{4}{3}} + \frac{24}{11} x^{\frac{11}{6}} + \frac{3}{7} x^{\frac{7}{3}} + c$

$3 x^{\frac{3}{4}} + \frac{24}{11} x^{\frac{11}{6}} + \frac{3}{7} x^{\frac{7}{3}} + c$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\int x^{\frac{1}{3}} {(2 + x^{\frac{1}{2}})}^{2} d x$

$Let x = t^{6}$

$\begin{array}{l} d x = 6 t^{5} d t \\ = \int t^{2} {(2 + t^{3})}^{2} 6 t^{5} d t \\ = 6 \int t^{7} (4 + t^{6} + 4 t^{3}) d t \\ = 6 \int (4 t^{7} + 4 t^{10} + t^{13}) d t \\ = 6 \int (4 \frac{t^{8}}{8} + 4 \frac{t^{11}}{11} + \frac{t^{14}}{14}) + C \\ = 3 x^{\frac{4}{3}} + \frac{24}{11} x^{\frac{11}{6}} + \frac{3}{7} \cdot x^{\frac{7}{3}} + C \end{array}$