Download App

Indefinite Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIndefinite Integrals2 Marks
Question
Evaluate $\int\frac{1}{\text{x}^2+16}\text{ dx}$
✓

Answer

Since, $\int\frac{1}{\text{x}^2+\text{a}^2}\text{ dx}=\frac{1}{\text{a}}\tan^{-1}\Big(\frac{\text{x}}{\text{a}}\Big)+\text{C}$
Thus, $\int\frac{1}{\text{x}^2+16}\text{ dx}=\frac{1}{4}\tan^{-1}\Big(\frac{\text{x}}{4}\Big)+\text{C}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

For the principal values, evaluate the following:
$\cos^{-1}\frac{1}{2}+2\sin^{-1}\Big(\frac{1}{2}\Big)$
→
Differentiate the ${e^x} + {e^{{x^2}}} + ... + {e^{{x^5}}}$ w.r.t. x.
→
Find the sum of the following vectors: $\vec{\text{a}}=\hat{\text{i}}-2\hat{\text{j}},\vec{\text{b}}=2\hat{\text{i}}-3\hat{\text{j}},\vec{\text{c}}=2\hat{\text{i}}-3\hat{\text{k}}$.
→
Evaluate the following determinant:
$\begin{vmatrix}1&-3&2\\4&-1&2\\3&5&2\end{vmatrix}$
→
If $\vec{\text{a}},\vec{\text{b}}$ are two vectors, then write the truth value of the following statement:$\big|\vec{\text{a}}\big|=\big|\vec{\text{b}}\big|\Rightarrow\vec{\text{a}}=\vec{\text{b}}$
→
Find the integral of the function $\frac{{\cos x}}{{1 + \cos x}}$
→
Differentiate $(x^2– 5x + 8) (x^3 + 7x + 9)$ in three ways mentioned below:
by expanding the product to obtain a single polynomial.
→
Find X, if Y = $\left[\begin{array}{ll} {3} & {2} \\ {1} & {4} \end{array}\right] \text { and } 2 \mathrm{X}+\mathrm{Y}=\left[\begin{array}{rr} {1} & {0} \\ {-3} & {2} \end{array}\right]$
→
Check the injectivity and surjectivity of the following functions:
$f: N → N$ given by $f(x) = x^2$
→
Integrate the function in Exercise.
$\sqrt{4-\text{x}^2}$
→