12. Sınıf Belirsiz İntegral Ödev Hazırla

12. Sınıf – Belirsiz İntegral

Adı Soyadı:

Sınıfı:

No:

Tarih / Puan:

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

A) \(-3\ln|-x+2| + C\) B) \(3-x+2 + C\) C) \(-(3\ln|-x+2|) + C\) D) \(\ln|-x+2| + C\) E) \(3\ln|-x+2| + C\)

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

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

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

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

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

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

5) Aşağıdaki belirsiz integrali bulunuz (trig dönüşüm):
\(\int \sqrt{7^2-x^2}\,dx\)

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

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

A) \(-\frac{2}{3}3x+1 + C\) B) \(-(-\frac{2}{3}\ln|3x+1|) + C\) C) \(-\frac{2}{3}\ln|3x+1| + C\) D) \(-2\ln|3x+1| + C\) E) \(\ln|3x+1| + C\)

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

A) \(-\ln|4x+2| + C\) B) \(-4\ln|4x+2| + C\) C) \(\ln|4x+2| + C\) D) \(-14x+2 + C\) E) \(-(-\ln|4x+2|) + C\)

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

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

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

A) \(x^{-3} + C\) B) \(-\frac{1}{x^{2}} + C\) C) \(-2x^{-2} + C\) D) \(\frac{1}{x^{2}} + C\) E) \(x^{-1} + C\)

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

A) \(-\frac{4}{3}\frac{1}{x^{3}} + C\) B) \(\frac{4}{3}\frac{1}{x^{3}} + C\) C) \(\frac{4}{3}x^{-2} + C\) D) \(\frac{4}{3}x^{-4} + C\) E) \(-4x^{-3} + C\)

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

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

12) Aşağıdaki belirsiz integrali bulunuz:
\(\int 2\sin(-x+1)\,dx\)

A) \(2\cos(x) + C\) B) \(-2\cos(-x+1) + C\) C) \(-(2\cos(-x+1)) + C\) D) \(2\cos(-x+1) + C\) E) \(2\sin(-x+1) + C\)

13) Aşağıdaki belirsiz integrali bulunuz (trig dönüşüm):
\(\int \sqrt{9^2-x^2}\,dx\)

A) \(\frac{x}{2}\sqrt{9^2-x^2} - \frac{9^2}{2}\arcsin\left(\frac{x}{9}\right) + C\) B) \(x\sqrt{9^2-x^2} + 9^2\arcsin\left(\frac{x}{9}\right) + C\) C) \(\frac{x}{2}\sqrt{9^2-x^2} + \frac{9}{2}\arcsin\left(\frac{x}{9}\right) + C\) D) \(\frac{x}{2}\sqrt{9^2-x^2} + \frac{9^2}{2}\arcsin\left(\frac{x}{9}\right) + C\) E) \(\sqrt{9^2-x^2} + C\)

14) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{2}{x^2+5^2}\,dx\)

A) \(\frac{2}{25}\arctan\left(\frac{x}{5}\right) + C\) B) \(\frac{2}{5}\ln|x^2+5^2| + C\) C) \(\frac{2}{5}\arctan\left(\frac{x}{5}\right) + C\) D) \(-(\frac{2}{5}\arctan\left(\frac{x}{5}\right)) + C\) E) \(\frac{2}{5}\arctan(x) + C\)

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

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

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

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

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

A) \(-2x + C\) B) \(\ln x + C\) C) \(-(-2\ln|x|) + C\) D) \(\frac{-2}{x} + C\) E) \(-2\ln|x| + C\)

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

A) \(-(-\tan(4x+5)) + C\) B) \(-1\sec(4x+5) + C\) C) \(-4\tan(4x+5) + C\) D) \(-1\cot(4x+5) + C\) E) \(-\tan(4x+5) + C\)

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

A) \(\frac{2}{3}\arctan(x) + C\) B) \(\frac{1}{9}\arctan\left(\frac{x}{6}\right) + C\) C) \(\frac{2}{3}\arctan\left(\frac{x}{6}\right) + C\) D) \(-(\frac{2}{3}\arctan\left(\frac{x}{6}\right)) + C\) E) \(\frac{2}{3}\ln|x^2+6^2| + C\)

20) Aşağıdaki belirsiz integrali bulunuz (parçalı rasyonel):
\(\int \frac{2}{x^2-6^2}\,dx\)

A) \(\frac{1}{6}\ln|x^2-6^2| + C\) B) \(\frac{1}{6}\ln\left|\frac{x-6}{x+6}\right| + C\) C) \(\frac{1}{6}\ln\left|\frac{x+6}{x-6}\right| + C\) D) \(\frac{1}{3}\ln\left|\frac{x-6}{x+6}\right| + C\) E) \(-(\frac{1}{6}\ln\left|\frac{x-6}{x+6}\right|) + C\)