Download App

Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
Question
$\int \frac{10 x^{9}+10^{x} \log _{e} 10 d x}{x^{10}+10^{x}}$,  equals
✓

Answer

Let x10 + 10x = t
$\Rightarrow$ (10x9 + 10x loge10)dx = dt
$\Rightarrow \int \frac{10 x^{9}+10^{x} \log _{e} 10}{x^{10}+10^{x}} d x=\int \frac{d t}{t}$ 
= log t + C
= log(x10 + 10x) + 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 "1 Marks" from Integrals→Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The vector directed from A to B and joining the points $A (1,2,2)$ and $B (2,3,1)$ is :
→
Find an anti derivative (or integral) of the following function by the method of inspection.
$\sin2\text{x}$
→
What is the range of the function f(x) = $\frac{|{x-1}|}{({x-1)}}?$
→
Find the order and degree, if defined, of the differential equation $x y \frac{d^{2} y}{d x^{2}}+x\left(\frac{d y}{d x}\right)^{2}-y \frac{d y}{d x}=0$
→
Integrate the functions in Exercises:
$\sqrt{\text{ax+b}}$
→
Integrate the functions in Exercises:
$\frac{1}{\text{x}-\sqrt{\text{x}}}$
→
Discuss the continuity of the function $f$, where $f$ is defined by $f(x)=\left\{\begin{array}{ll}-2 & , \text { if } x \leq-1 \\ 2 x & , \text { if }-1 < x \leq 1 \\ 2 & , \text { if } x > 1\end{array}\right.$
→
Write an anti derivative of function cos 2x using the method of inspection.
→
Evaluate the following:
$\cot^{-1}\Big(\cot\frac{\pi}{3}\Big)$
→
Write the order of the differrntial quation associated with the primitive $\text{y}=\text{C}_{1}+\text{C}_{2}\text{e}^{\text{x}}+\text{C}_{3}\text{e}^{-2\text{x}+\text{C}_{4}}$ where C1, C2, C3, C4 are arbitrary constants.
→