作业帮求积分 (tanx^2+tanx^4 )dx
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求积分 (tanx^2+tanx^4 )dx
求积分 (tanx^2+tanx^4 )dx
求积分 (tanx^2+tanx^4 )dx
S((tanx)^2+(tanx)^4 )dx
=S(tanx)^2(1+(tanx)^2)dx
=S(tanx)^2 *(secx)^2)dx
=S(tanx)^2 d(tanx)
=1/3*tan(x)^3+C
∫(tanx^2+tanx^4 )dx
=∫(sec²x-1+(sec²x-1)²)dx
=∫(sec²x-1+sec^4x-2sec²x+1)dx
=∫(sec^4x-sec²x)dx
=∫sec²xdtanx-tanx
=∫(tan²x+1)dtanx-tanx
=1/3tan³x+tanx-tanx+c
=1/3tan³x+c
∫tanx^2 dx = ∫[(secx)^2 -1] dx =tanx - x + C
∫(tanx^2+tanx^4)dx
=∫[(secx)^2 -1] dx +∫(tanx)^2 *[(secx)^2 -1] dx
=tanx - x+∫tanx^2 * (secx)^2 dx - ∫(tanx)^2 dx
=tanx - x+∫...
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∫tanx^2 dx = ∫[(secx)^2 -1] dx =tanx - x + C
∫(tanx^2+tanx^4)dx
=∫[(secx)^2 -1] dx +∫(tanx)^2 *[(secx)^2 -1] dx
=tanx - x+∫tanx^2 * (secx)^2 dx - ∫(tanx)^2 dx
=tanx - x+∫tanx^2 d(tanx) - ∫[(secx)^2 -1 ]dx
=tanx - x+tanx^3/3 - ∫(secx)^2 dx +∫ 1 dx
=tanx - x+tanx^3/3 -tanx + x + C
=1/3tanx^3+C
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