∫ln(1+x²)/x³dx的不定积分
问题描述:
∫ln(1+x²)/x³dx的不定积分
答
∫ln(1+x²)/x³dx= -1/2∫ln(1+x²)d(1/x²)=-1/2(ln(1+x²))/x²)+1/2∫1/(x²(1+x²))dx²=-1/2(ln(1+x²))/x²)+1/2∫(1/x²-1/(1+x²))dx...
∫ln(1+x²)/x³dx的不定积分
∫ln(1+x²)/x³dx= -1/2∫ln(1+x²)d(1/x²)=-1/2(ln(1+x²))/x²)+1/2∫1/(x²(1+x²))dx²=-1/2(ln(1+x²))/x²)+1/2∫(1/x²-1/(1+x²))dx...