$$$\left(- \tan{\left(x \right)} + \sec{\left(x \right)}\right) \sec{\left(x \right)}$$$'nin integrali
İlgili hesap makinesi: Belirli ve Uygunsuz İntegral Hesaplayıcı
Girdiniz
Bulun: $$$\int \left(- \tan{\left(x \right)} + \sec{\left(x \right)}\right) \sec{\left(x \right)}\, dx$$$.
Çözüm
Expand the expression:
$${\color{red}{\int{\left(- \tan{\left(x \right)} + \sec{\left(x \right)}\right) \sec{\left(x \right)} d x}}} = {\color{red}{\int{\left(- \tan{\left(x \right)} \sec{\left(x \right)} + \sec^{2}{\left(x \right)}\right)d x}}}$$
Her terimin integralini alın:
$${\color{red}{\int{\left(- \tan{\left(x \right)} \sec{\left(x \right)} + \sec^{2}{\left(x \right)}\right)d x}}} = {\color{red}{\left(- \int{\tan{\left(x \right)} \sec{\left(x \right)} d x} + \int{\sec^{2}{\left(x \right)} d x}\right)}}$$
$$$\sec^{2}{\left(x \right)}$$$'nin integrali $$$\int{\sec^{2}{\left(x \right)} d x} = \tan{\left(x \right)}$$$:
$$- \int{\tan{\left(x \right)} \sec{\left(x \right)} d x} + {\color{red}{\int{\sec^{2}{\left(x \right)} d x}}} = - \int{\tan{\left(x \right)} \sec{\left(x \right)} d x} + {\color{red}{\tan{\left(x \right)}}}$$
$$$\tan{\left(x \right)} \sec{\left(x \right)}$$$'nin integrali $$$\int{\tan{\left(x \right)} \sec{\left(x \right)} d x} = \sec{\left(x \right)}$$$:
$$\tan{\left(x \right)} - {\color{red}{\int{\tan{\left(x \right)} \sec{\left(x \right)} d x}}} = \tan{\left(x \right)} - {\color{red}{\sec{\left(x \right)}}}$$
Dolayısıyla,
$$\int{\left(- \tan{\left(x \right)} + \sec{\left(x \right)}\right) \sec{\left(x \right)} d x} = \tan{\left(x \right)} - \sec{\left(x \right)}$$
İntegrasyon sabitini ekleyin:
$$\int{\left(- \tan{\left(x \right)} + \sec{\left(x \right)}\right) \sec{\left(x \right)} d x} = \tan{\left(x \right)} - \sec{\left(x \right)}+C$$
Cevap
$$$\int \left(- \tan{\left(x \right)} + \sec{\left(x \right)}\right) \sec{\left(x \right)}\, dx = \left(\tan{\left(x \right)} - \sec{\left(x \right)}\right) + C$$$A