#### Integration problem 2

Integral taken from instagram user @integralsforyou

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\int\tan^2(x)\cdot\sin(x)dx |

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=\int\frac{\sin^2(x)}{\cos^2(x)}\cdot\sin(x)dx |

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=\int\frac{\sin(x)\cdot(1-\cos^2(x))}{\cos^2(x)}dx |

let u=\cos(x)

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du=-\sin(x)dx |

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=-\int\frac{1-u^2}{u^2}du |

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=-\int(\frac{1}{u^2}-\frac{u^2}{u^2})du |

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=\int(1-\frac{1}{u^2})du |

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=u+\frac{1}{u}+C |

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=\cos(x)+\sec(x)+C |