Integrate (5-3sqrtx)^2 dx?

1 Answer
Mar 4, 2018

#int(5-3sqrtx)2dx=9/2x^2+25x-20x^(3/2)+"c"#

Explanation:

#int(5-3sqrtx)^2dx#

Expand the brackets using the perfect square formula

#=int25-30sqrtx+9xdx#

Split the integral and integrate term-by-term using the power rule

#=int25dx -30intx^(1/2)dx+9intxdx#

=#25x-20x^(3/2)+9/2x^2+"c"#