12. Sınıf Belirsiz İntegral Ödev Hazırla

12. Sınıf – Belirsiz İntegral

Adı Soyadı:

Sınıfı:

No:

Tarih / Puan:

1) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{6}{1+x^2}\,dx\)

A) \(6\tan x + C\) B) \(6\ln|1+x^2| + C\) C) \(-(6\arctan x) + C\) D) \(\arcsin x + C\) E) \(6\arctan x + C\)

2) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{4}{x^2+3^2}\,dx\)

A) \(\frac{4}{9}\arctan\left(\frac{x}{3}\right) + C\) B) \(\frac{4}{3}\arctan\left(\frac{x}{3}\right) + C\) C) \(\frac{4}{3}\ln|x^2+3^2| + C\) D) \(\frac{4}{3}\arctan(x) + C\) E) \(-(\frac{4}{3}\arctan\left(\frac{x}{3}\right)) + C\)

3) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{1}{\sqrt{x^2+2^2}}\,dx\)

A) \(\arcsin\left(\frac{x}{2}\right) + C\) B) \(\sqrt{x^2+2^2} + C\) C) \(\ln\left|x+\sqrt{x^2-2^2}\right| + C\) D) \(\ln|x| + C\) E) \(\ln\left|x+\sqrt{x^2+2^2}\right| + C\)

4) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{-2}{1+x^2}\,dx\)

A) \(-2\ln|1+x^2| + C\) B) \(-2\arctan x + C\) C) \(\arcsin x + C\) D) \(-2\tan x + C\) E) \(-(-2\arctan x) + C\)

5) Aşağıdaki belirsiz integrali bulunuz:
\(\int -\frac{1}{x}\,dx\)

A) \(-1x + C\) B) \(-(-\ln|x|) + C\) C) \(\ln x + C\) D) \(-\ln|x| + C\) E) \(\frac{-1}{x} + C\)

6) Aşağıdaki belirsiz integrali bulunuz:
\(\int -4(-4x-6)^{-2}\,dx\)

A) \(-(-4x-6)^{-2} + C\) B) \(4(-4x-6)^{-1} + C\) C) \(-(-4x-6)^{-1} + -6 + C\) D) \((-4x-6)^{-1} + C\) E) \(-(-4x-6)^{-1} + C\)

7) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{1}{\sqrt{x^2+7^2}}\,dx\)

A) \(\ln|x| + C\) B) \(\ln\left|x+\sqrt{x^2-7^2}\right| + C\) C) \(\ln\left|x+\sqrt{x^2+7^2}\right| + C\) D) \(\arcsin\left(\frac{x}{7}\right) + C\) E) \(\sqrt{x^2+7^2} + C\)

8) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{-2}{x^2+3^2}\,dx\)

A) \(-\frac{2}{9}\arctan\left(\frac{x}{3}\right) + C\) B) \(-\frac{2}{3}\arctan\left(\frac{x}{3}\right) + C\) C) \(-\frac{2}{3}\ln|x^2+3^2| + C\) D) \(-(-\frac{2}{3}\arctan\left(\frac{x}{3}\right)) + C\) E) \(-\frac{2}{3}\arctan(x) + C\)

9) Aşağıdaki belirsiz integrali bulunuz:
\(\int -4\sec^2(2x-5)\,dx\)

A) \(-(-2\tan(2x-5)) + C\) B) \(-4\tan(2x-5) + C\) C) \(-2\tan(2x-5) + C\) D) \(-2\sec(2x-5) + C\) E) \(-2\cot(2x-5) + C\)

10) Aşağıdaki belirsiz integrali bulunuz:
\(\int -35^{-4x-2}\,dx\)

A) \(\frac{3}{4}5^{-4x-2} + C\) B) \(\frac{3}{4\ln 5}5^{x} + C\) C) \(\frac{-3}{\ln 5}5^{-4x-2} + C\) D) \(\frac{3}{4\ln 5}5^{-4x-2} + C\) E) \(-(\frac{3}{4\ln 5}5^{-4x-2}) + C\)

11) Aşağıdaki belirsiz integrali bulunuz:
\(\int -e^{-3x-1}\,dx\)

A) \(\frac{1}{3}(-3x-1)e^{-3x-1} + C\) B) \(\frac{1}{3}e^{-3x-1} + C\) C) \(-1e^{-3x-1} + C\) D) \(\frac{1}{3}e^{x} + C\) E) \(-(\frac{1}{3}e^{-3x-1}) + C\)

12) Aşağıdaki belirsiz integrali bulunuz:
\(\int 3\sin(x-4)\,dx\)

A) \(-3\cos(x) + C\) B) \(-3\cos(x-4) + C\) C) \(-3\sin(x-4) + C\) D) \(-(-3\cos(x-4)) + C\) E) \(3\cos(x-4) + C\)

13) Aşağıdaki belirsiz integrali bulunuz:
\(\int 47^{-2x-3}\,dx\)

A) \(\frac{-2}{\ln 7}7^{-2x-3} + C\) B) \(-(\frac{-2}{\ln 7}7^{-2x-3}) + C\) C) \(\frac{4}{\ln 7}7^{-2x-3} + C\) D) \(\frac{-2}{\ln 7}7^{x} + C\) E) \(-27^{-2x-3} + C\)

14) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{-3}{\sqrt{1-x^2}}\,dx\)

A) \(-3\ln|1-x^2| + C\) B) \(-3\sin x + C\) C) \(\arctan x + C\) D) \(-(-3\arcsin x) + C\) E) \(-3\arcsin x + C\)

15) Aşağıdaki belirsiz integrali bulunuz (trig dönüşüm):
\(\int \sqrt{3^2-x^2}\,dx\)

A) \(\frac{x}{2}\sqrt{3^2-x^2} + \frac{3}{2}\arcsin\left(\frac{x}{3}\right) + C\) B) \(\sqrt{3^2-x^2} + C\) C) \(\frac{x}{2}\sqrt{3^2-x^2} - \frac{3^2}{2}\arcsin\left(\frac{x}{3}\right) + C\) D) \(\frac{x}{2}\sqrt{3^2-x^2} + \frac{3^2}{2}\arcsin\left(\frac{x}{3}\right) + C\) E) \(x\sqrt{3^2-x^2} + 3^2\arcsin\left(\frac{x}{3}\right) + C\)

16) Aşağıdaki belirsiz integrali bulunuz:
\(\int -45^{-x}\,dx\)

A) \(-(\frac{4}{\ln 5}5^{-x}) + C\) B) \(\frac{4}{\ln 5}5^{-x} + C\) C) \(45^{-x} + C\) D) \(\frac{-4}{\ln 5}5^{-x} + C\) E) \(\frac{4}{\ln 5}5^{x} + C\)

17) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{2}{-2x-1}\,dx\)

A) \(-(-\ln|-2x-1|) + C\) B) \(-\ln|-2x-1| + C\) C) \(2\ln|-2x-1| + C\) D) \(-1-2x-1 + C\) E) \(\ln|-2x-1| + C\)

18) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{-3}{1+x^2}\,dx\)

A) \(-3\tan x + C\) B) \(-3\ln|1+x^2| + C\) C) \(-3\arctan x + C\) D) \(\arcsin x + C\) E) \(-(-3\arctan x) + C\)

19) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{2}{1+x^2}\,dx\)

A) \(2\ln|1+x^2| + C\) B) \(2\tan x + C\) C) \(2\arctan x + C\) D) \(\arcsin x + C\) E) \(-(2\arctan x) + C\)

20) Aşağıdaki belirsiz integrali bulunuz:
\(\int 1\,dx\)

A) \((2x+4) + C\) B) \(\frac{1}{2}(2x+4) + 4 + C\) C) \(\frac{1}{2}(2x+4)^{0} + C\) D) \(\frac{1}{2}(2x+4) + C\) E) \(-\frac{1}{2}(2x+4) + C\)