12. Sınıf Belirsiz İntegral Ödev Hazırla

12. Sınıf – Belirsiz İntegral

Adı Soyadı:

Sınıfı:

No:

Tarih / Puan:

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

A) \(3\sec(-2x-4) + C\) B) \(3\cot(-2x-4) + C\) C) \(-(3\tan(-2x-4)) + C\) D) \(-6\tan(-2x-4) + C\) E) \(3\tan(-2x-4) + C\)

2) Aşağıdaki belirsiz integrali bulunuz (parçalı rasyonel):
\(\int \frac{-2x+2}{\left(x-5\right)\left(x-3\right)}\,dx\)

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

3) Aşağıdaki belirsiz integrali bulunuz:
\(\int -4\cos(x+2)\,dx\)

A) \(4\sin(x+2) + C\) B) \(-4\sin(x+2) + C\) C) \(-4\cos(x+2) + C\) D) \(-4\sin(x) + C\) E) \(-(-4\sin(x+2)) + C\)

4) Aşağıdaki belirsiz integrali bulunuz (parçalı rasyonel):
\(\int \frac{-x-13}{\left(x-2\right)\left(x+3\right)}\,dx\)

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

5) Aşağıdaki belirsiz integrali bulunuz:
\(\int \frac{1}{\sqrt{x^2-5^2}}\,dx\)

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

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

A) \(6\ln|x| + C\) B) \(-(6\ln|x|) + C\) C) \(\frac{6}{x} + C\) D) \(\ln x + C\) E) \(6x + C\)

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

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

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

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

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

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

10) Aşağıdaki belirsiz integrali bulunuz:
\(\int 6\sin(2x-5)\,dx\)

A) \(3\cos(2x-5) + C\) B) \(-3\sin(2x-5) + C\) C) \(-3\cos(2x-5) + C\) D) \(6\cos(2x-5) + C\) E) \(-(-3\cos(2x-5)) + C\)

11) Aşağıdaki belirsiz integrali bulunuz:
\(\int e^{-2x+5}\,dx\)

A) \(-\frac{1}{2}(-2x+5)e^{-2x+5} + C\) B) \(-(-\frac{1}{2}e^{-2x+5}) + C\) C) \(1e^{-2x+5} + C\) D) \(-\frac{1}{2}e^{x} + C\) E) \(-\frac{1}{2}e^{-2x+5} + C\)

12) Aşağıdaki belirsiz integrali bulunuz:
\(\int -65^{-4x-2}\,dx\)

A) \(\frac{3}{2\ln 5}5^{-4x-2} + C\) B) \(-(\frac{3}{2\ln 5}5^{-4x-2}) + C\) C) \(\frac{-6}{\ln 5}5^{-4x-2} + C\) D) \(\frac{3}{2}5^{-4x-2} + C\) E) \(\frac{3}{2\ln 5}5^{x} + C\)

13) Aşağıdaki belirsiz integrali bulunuz:
\(\int -3\cos(4x+5)\,dx\)

A) \(-(-\frac{3}{4}\sin(4x+5)) + C\) B) \(-\frac{3}{4}\sin(4x+5) + C\) C) \(-3\sin(4x+5) + C\) D) \(\frac{3}{4}\sin(4x+5) + C\) E) \(-\frac{3}{4}\cos(4x+5) + C\)

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

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

15) Aşağıdaki belirsiz integrali bulunuz:
\(\int 4e^{x+5}\,dx\)

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

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

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

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

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

18) Aşağıdaki belirsiz integrali bulunuz:
\(\int 45^{3x-5}\,dx\)

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

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

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

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

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