how to integrate [x^5(1+x^4)]

Dear student,

Let x4=t

then 4x3 dx=dt

Substitute these values and you will easliy integrate it using standard results...

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

it is ur soln.

x^5(1+x^4) dx

(x^5+x^9) dx

which on integration gives

x^6 .1/6+x^10 .1/10

[1+x⁴]x⁵dx = [1+x⁴]x²x³ dx

put   x⁴ = t

       4x³dx = dt

now expression is

 [1+t]t^1/2 dt/4

[ t^1/2+t^3/2 ]dt/4

[(2/3)t^3/2 + (2/5)t^5/2]/4 + C

(2/3)(x⁶) + (2/5)x¹⁰ + C