What is #\int ( 4x ^ { 3} + \cos x ) d x#?

1 Answer
Yousef A.
Feb 7, 2018

#x^4+sinx#

Explanation:

#inta+b# = #int a#+#intb#
#int4x^3dx##+##intcosxdx#
use the reverse power rule to integrate #4x^3#
#intmx^n#=#int(mx^(n+1))/(n+1)#
since #d/dx sinx=cosx#, you can reverse it to integrate #cosx#
so, #int4x^3dx##+##intcosxdx#
= #4(x^4)/4#+#sinx#
= #x^4+sinx#

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