How do you find int(x^2-1/x^2+root3x)dx(x21x2+3x)dx?

2 Answers
Apr 13, 2017

=x^3/3+1/x+3/4x^(4/3)+C=x33+1x+34x43+C

Explanation:

int(x^2-1/x^2+root(3)(x)) dx(x21x2+3x)dx

By rewriting,

=int(x^2-x^(-2)+x^(1/3)) dx=(x2x2+x13)dx

By the Power Rule for integration, which states that intx^ndx=x^(n+1)/(n+1)+Cxndx=xn+1n+1+C:

=x^3/3-x^(-1)/(-1)+x^(4/3)/(4/3)+C=x33x11+x4343+C

By cleaning up,

=x^3/3+1/x+3/4x^(4/3)+C=x33+1x+34x43+C

I hope that this was clear.

Apr 13, 2017

1/3x^3+1/x+3/4x^(4/3)+c13x3+1x+34x43+c

Explanation:

integrate each term using the color(blue)"power rule for integration"power rule for integration

• int(ax^n)=a/(n+1)x^(n+1) ; n!=-1(axn)=an+1xn+1;n1

rArrint(x^2-1/x^2+root(3)(x))dx(x21x2+3x)dx

=int(x^2-x^-2+x^(1/3))larr" in exponent form"=(x2x2+x13) in exponent form

=1/3x^3+1/x+3/4x^(4/3)+c=13x3+1x+34x43+c

where c is the constant of integration.