Question

(sinx)^3+(cosx)^3求积分

Answer 1

方便起见,积分符号写成J
J[(sinx)^3+(cosx)^3]dx=J(sinx)^3dx+J(cosx)^3dx=-J（1-cos^2x）dcosx+J（1-sin^2x）dsinx=-cosx-(cosx)^3/3+sinx-(sinx)^3/3+C

Answer 2

∫(sinx)^3dx=∫-(sinx)^2dcosx=∫[(cosx)^2-1]dcosx=(cosx)^3/3-cosx
∫(cosx)^3dx=∫(cosx)^2dsinx=∫[1-(sinx)^2]dsinx=sinx-(sinx)^3/3+C
∫[(sinx)^3+(cosx)^3]dx=sinx-cosx+(cosx)^3/3-(sinx)^3/3+C

Answer 3

(sinx)^3+(cosx)^3求积分
3(sinx)^2 *cosx +3(cosx)^2 *(-sinx)

Answer 4

4/1(sinx)^4-4/1(cosx)^4