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Question

$$\int {{{\sec }^2}\left( {7 - 4x} \right)} dx$$


A
14tan2(74x)+C
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B
14tan(74x)+C
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C
116tan(74x)+C
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D
18tan2(74x)+C
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Solution

The correct option is A $$\dfrac {-1}{4}\tan (7-4x)+C$$
$${\sec ^2}\left( {7 - 4x} \right)dx$$
$$let{\text{   7 -  4x  =  t}}$$
$${\text{then   - 4dx  =  dt}}$$
$$\int {{{\sec }^2}t} {\text{  }}\dfrac{{dt}}{{ - 4}}$$
$$= - \dfrac{1}{4}\int {{{\sec }^2}{\text{t}}\;d{\text{t}}} $$

$$= - \dfrac{1}{4}{\text{ tant  +  c}}$$

$$=- \dfrac{1}{4}\tan {\text{ }}\left( {7 - 4x} \right){\text{  +  c}}$$

Mathematics

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