Consider the following statements:Assertion ( | vedclass

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(C) Assertion $(A)$ is true because the integral $\int \frac{1}{x^2 + a^2} dx$ can be solved by substituting $x = a 	an 	heta$,which gives $dx = a \

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$A$ is true but $R$ is false.

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(C) Assertion $(A)$ is true because the integral $\int \frac{1}{x^2 + a^2} dx$ can be solved by substituting $x = a 	an 	heta$,which gives $dx = a \sec^2 	heta d	heta$. Substituting these into the integral yields $\int \frac{a \sec^2 	heta}{a^2 	an^2 	heta + a^2} d	heta = \int \frac{a \sec^2 	heta}{a^2 \sec^2 	heta} d	heta = \frac{1}{a} \int d	heta = \frac{1}{a} 	heta + C = \frac{1}{a} 	an^{-1}(\frac{x}{a}) + C$.Reason $(R)$ is false because not all integrands can be integrated by the method of substitution. There are many other methods such as integration by parts,partial fractions,and direct standard formulas.Therefore,$A$ is true but $R$ is false.

Consider the following statements:
Assertion $(A):$ $\frac{1}{x^2 + a^2}$ can be integrated by a substitution $x = a \tan \theta$.
Reason $(R):$ Because all integrands are integrated by the method of substitution only.
Which of the following is correct?

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Consider the following statements:Assertion $(A):$ $\frac{1}{x^2 + a^2}$ can be integrated by a substitution $x = a \tan \theta$.Reason $(R):$ Because all integrands are integrated by the method of substitution only.Which of the following is correct?