Question

求解不定积分2-6

求2-6不定积分解题步骤

Answer 1

2.原式=∫（1/2√x）*(6/x)dx
=6∫(1/x)d√x
=6∫(1/(√x)^2)d√x
=-6/√x+C
4.原式=∫(2/5)/(x+3/5)dx
=2/5∫1/(x+3/5)d(x+3/5)
=2/5*ln(x+3/5)+C
5.原式=1/3∫3x^2*e^(x^3)dx
=1/3∫e^(x^3)d(x^3)
=1/3*e^(x^3)+C
6.原式=1/4∫4x*cos(2x+3)dx
=1/2∫cos(2x^2+3)d(2x^2)
=1/2∫cos(2x^2+3)d(2x^2+3)
=-1/2*sin(2x^2+3)+C

Answer 2

(2) 原式 = ∫3x^(-3/2)dx = 3(-2)x^(-1/2) + C = -6/√x + C
(3) 原式 = ∫(5/7)^xdx = (5/7)^x/ln(5/7) + C = [1/(ln5-ln7)](5^x/7^x) + C
(4) 原式 = ∫[2/(5x+3)]dx = (2/5)∫d(5x+3)/(5x+3) = (2/5)ln|5x+3| + C
(5) 原式 = ∫x^2e^(x^3)dx = (1/3)∫e^(x^3)d(x^3) = (1/3)e^(x^3) + C
(6) 原式 = ∫xcos(2x^2+3)dx = (1/4)∫cos(2x^2+3)d(2x^2+3)
= (1/4)sin(2x^2+3) + C