أجد التكامل: (3x + 4)/(x2 + x) dx.

نحلل x2+x=x(x+1)، ثم (3x+4)/(x(x+1))=(4)/(x)-(1)/(x+1)؛ إذن التكامل 4|x|-|x+1|+C. يراجع تحليل المقام قبل كتابة الصورة الجزئية.

التكامل بالكسور الجزئية: Mathematics Tawjihi question with answer

A Tawjihi Mathematics question (التكامل) with the answer and worked steps.

From the Tawjihi question bank: Mathematics · التكامل

أجد التكامل: $\int \frac{3x + 4}{x^2 + x} dx$ .

التكامل بالكسور الجزئية

The answer

نحلل

x^2+x=x(x+1)

، ثم

\frac{3x+4}{x(x+1)}=\frac{4}{x}-\frac{1}{x+1}

؛ إذن التكامل

4\ln|x|-\ln|x+1|+C

.

Explanation

يراجع تحليل المقام قبل كتابة الصورة الجزئية.

Let Zaki explain it another way

The answer above is completely free. When you sign in, Zaki can explain this question a different way, give you ten more like it on the same lesson, and track your progress in the subject.

Practise more like this

Keep going

All Mathematics questions Mathematics hub Official past papers

Sign up now and plan your post-results step with Zaki — no invented ministry dates.

Start with Zaki Start with Zaki

Sign up now and plan your post-results step with Zaki — no invented ministry dates.

Start with Zaki Start with Zaki

التكامل بالكسور الجزئية: Mathematics Tawjihi question with answer